Apply Properties of Integer Exponents - 8th Grade Math
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What is the simplified form of $(4 \cdot 7)^2$?
What is the simplified form of $(4 \cdot 7)^2$?
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$4^2 \cdot 7^2$. Using power of a product rule: $(4 \cdot 7)^2 = 4^2 \cdot 7^2$.
$4^2 \cdot 7^2$. Using power of a product rule: $(4 \cdot 7)^2 = 4^2 \cdot 7^2$.
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What is the value of $(3^2)^4$?
What is the value of $(3^2)^4$?
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$3^8$. Power of a power: $(3^2)^4 = 3^{2 \cdot 4} = 3^8$.
$3^8$. Power of a power: $(3^2)^4 = 3^{2 \cdot 4} = 3^8$.
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What is the value of $\frac{5^9}{5^2}$?
What is the value of $\frac{5^9}{5^2}$?
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$5^7$. Quotient rule: $\frac{5^9}{5^2} = 5^{9-2} = 5^7$.
$5^7$. Quotient rule: $\frac{5^9}{5^2} = 5^{9-2} = 5^7$.
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State the power of a product rule for $ (ab)^n $.
State the power of a product rule for $ (ab)^n $.
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$ (ab)^n = a^n b^n $. A power distributes over multiplication.
$ (ab)^n = a^n b^n $. A power distributes over multiplication.
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What is the value of $\left(\frac{4}{5}\right)^2$ written as a quotient of powers?
What is the value of $\left(\frac{4}{5}\right)^2$ written as a quotient of powers?
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$\frac{4^2}{5^2}$. Power of a quotient: $(\frac{a}{b})^n = \frac{a^n}{b^n}$
$\frac{4^2}{5^2}$. Power of a quotient: $(\frac{a}{b})^n = \frac{a^n}{b^n}$
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State the product of powers rule for the same base $a^m \cdot a^n$.
State the product of powers rule for the same base $a^m \cdot a^n$.
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$a^m \cdot a^n = a^{m+n}$. When multiplying powers with the same base, add the exponents.
$a^m \cdot a^n = a^{m+n}$. When multiplying powers with the same base, add the exponents.
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What is the value of $2^3 \cdot 2^5$?
What is the value of $2^3 \cdot 2^5$?
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$2^8$. Product rule: $2^3 \cdot 2^5 = 2^{3+5} = 2^8$.
$2^8$. Product rule: $2^3 \cdot 2^5 = 2^{3+5} = 2^8$.
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What is the value of $(-1)^{13}$?
What is the value of $(-1)^{13}$?
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$-1$. $(-1)$ to an odd power equals $-1$.
$-1$. $(-1)$ to an odd power equals $-1$.
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What is the value of $(-1)^{12}$?
What is the value of $(-1)^{12}$?
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$1$. $(-1)$ to an even power equals $1$.
$1$. $(-1)$ to an even power equals $1$.
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What is the value of $1^{-5}$?
What is the value of $1^{-5}$?
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$1$. $1$ raised to any power equals $1$.
$1$. $1$ raised to any power equals $1$.
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State the power of a quotient rule for $\left(\frac{a}{b}\right)^n$ where $b \ne 0$.
State the power of a quotient rule for $\left(\frac{a}{b}\right)^n$ where $b \ne 0$.
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$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$. A power distributes over division.
$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$. A power distributes over division.
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State the quotient of powers rule for the same base $\frac{a^m}{a^n}$ where $a \ne 0$.
State the quotient of powers rule for the same base $\frac{a^m}{a^n}$ where $a \ne 0$.
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$\frac{a^m}{a^n} = a^{m-n}$. When dividing powers with the same base, subtract the exponents.
$\frac{a^m}{a^n} = a^{m-n}$. When dividing powers with the same base, subtract the exponents.
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State the power of a power rule for $(a^m)^n$.
State the power of a power rule for $(a^m)^n$.
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$(a^m)^n = a^{mn}$. When raising a power to a power, multiply the exponents.
$(a^m)^n = a^{mn}$. When raising a power to a power, multiply the exponents.
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What is the value of $(2 \cdot 7)^3$ written as a product of powers?
What is the value of $(2 \cdot 7)^3$ written as a product of powers?
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$2^3 \cdot 7^3$. Power of a product: $(ab)^n = a^n b^n$.
$2^3 \cdot 7^3$. Power of a product: $(ab)^n = a^n b^n$.
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What is the value of $3^2 \cdot 3^{-5}$ expressed with a positive exponent?
What is the value of $3^2 \cdot 3^{-5}$ expressed with a positive exponent?
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$\frac{1}{3^3}$. Product rule gives $3^{2+(-5)} = 3^{-3} = \frac{1}{3^3}$.
$\frac{1}{3^3}$. Product rule gives $3^{2+(-5)} = 3^{-3} = \frac{1}{3^3}$.
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What is the value of $10^{-3}$ expressed as a fraction?
What is the value of $10^{-3}$ expressed as a fraction?
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$\frac{1}{10^3}$. Negative exponent rule: $a^{-n} = \frac{1}{a^n}$.
$\frac{1}{10^3}$. Negative exponent rule: $a^{-n} = \frac{1}{a^n}$.
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What is the value of $\frac{2^{-4}}{2^{-1}}$ expressed with a positive exponent?
What is the value of $\frac{2^{-4}}{2^{-1}}$ expressed with a positive exponent?
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$\frac{1}{2^3}$. Quotient rule: $\frac{2^{-4}}{2^{-1}} = 2^{-4-(-1)} = 2^{-3} = \frac{1}{2^3}$.
$\frac{1}{2^3}$. Quotient rule: $\frac{2^{-4}}{2^{-1}} = 2^{-4-(-1)} = 2^{-3} = \frac{1}{2^3}$.
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Identify the equivalent expression for $\frac{a^7}{a^{10}}$ using integer exponent rules.
Identify the equivalent expression for $\frac{a^7}{a^{10}}$ using integer exponent rules.
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$a^{-3}$. Quotient rule: $\frac{a^7}{a^{10}} = a^{7-10} = a^{-3}$.
$a^{-3}$. Quotient rule: $\frac{a^7}{a^{10}} = a^{7-10} = a^{-3}$.
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Find the simplified form of $\left(\frac{x^3 y^{-2}}{x^{-1}}\right)$ using exponent rules.
Find the simplified form of $\left(\frac{x^3 y^{-2}}{x^{-1}}\right)$ using exponent rules.
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$x^4 y^{-2}$. Simplify: $\frac{x^3 y^{-2}}{x^{-1}} = x^{3-(-1)} y^{-2} = x^4 y^{-2}$.
$x^4 y^{-2}$. Simplify: $\frac{x^3 y^{-2}}{x^{-1}} = x^{3-(-1)} y^{-2} = x^4 y^{-2}$.
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State the negative exponent rule for $a^{-n}$ where $a \ne 0$ and $n$ is a positive integer.
State the negative exponent rule for $a^{-n}$ where $a \ne 0$ and $n$ is a positive integer.
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$a^{-n} = \frac{1}{a^n}$. A negative exponent means reciprocal with positive exponent.
$a^{-n} = \frac{1}{a^n}$. A negative exponent means reciprocal with positive exponent.
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What is $(5^2)^3$ written as a single power of $5$?
What is $(5^2)^3$ written as a single power of $5$?
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$5^6$. Power of a power: $5^{2 \times 3} = 5^6$.
$5^6$. Power of a power: $5^{2 \times 3} = 5^6$.
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What is $\frac{2^7}{2^3}$ written as a single power of $2$?
What is $\frac{2^7}{2^3}$ written as a single power of $2$?
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$2^4$. Quotient rule: $2^{7-3} = 2^4$.
$2^4$. Quotient rule: $2^{7-3} = 2^4$.
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What is $\left(\frac{3}{5}\right)^2$ written as a fraction with exponents removed?
What is $\left(\frac{3}{5}\right)^2$ written as a fraction with exponents removed?
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$\frac{9}{25}$. $\frac{3^2}{5^2} = \frac{9}{25}$.
$\frac{9}{25}$. $\frac{3^2}{5^2} = \frac{9}{25}$.
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What is the value of $a^0$ for $a \ne 0$?
What is the value of $a^0$ for $a \ne 0$?
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$a^0 = 1$. Any nonzero number to the zero power equals 1.
$a^0 = 1$. Any nonzero number to the zero power equals 1.
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What is the value of $3^2 \cdot 3^{-5}$ written as a single power of $3$?
What is the value of $3^2 \cdot 3^{-5}$ written as a single power of $3$?
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$3^{-3}$. Product rule: $3^{2+(-5)} = 3^{-3}$.
$3^{-3}$. Product rule: $3^{2+(-5)} = 3^{-3}$.
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What is the value of $3^{-3}$ written as a fraction in simplest form?
What is the value of $3^{-3}$ written as a fraction in simplest form?
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$\frac{1}{27}$. $3^{-3} = \frac{1}{3^3} = \frac{1}{27}$.
$\frac{1}{27}$. $3^{-3} = \frac{1}{3^3} = \frac{1}{27}$.
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What is $(2 \cdot 3)^4$ written using powers of $2$ and $3$?
What is $(2 \cdot 3)^4$ written using powers of $2$ and $3$?
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$2^4 \cdot 3^4$. Power of a product: distribute the exponent 4 to both factors.
$2^4 \cdot 3^4$. Power of a product: distribute the exponent 4 to both factors.
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State the negative exponent rule for $a^{-n}$ where $a \ne 0$ and $n$ is an integer.
State the negative exponent rule for $a^{-n}$ where $a \ne 0$ and $n$ is an integer.
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$a^{-n} = \frac{1}{a^n}$. A negative exponent means reciprocal with positive exponent.
$a^{-n} = \frac{1}{a^n}$. A negative exponent means reciprocal with positive exponent.
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What is the value of $\frac{a^m}{a^m}$ for $a \ne 0$?
What is the value of $\frac{a^m}{a^m}$ for $a \ne 0$?
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$\frac{a^m}{a^m} = 1$. Any nonzero expression divided by itself equals 1.
$\frac{a^m}{a^m} = 1$. Any nonzero expression divided by itself equals 1.
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What is $10^{-2}$ written as a fraction in simplest form?
What is $10^{-2}$ written as a fraction in simplest form?
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$\frac{1}{100}$. $10^{-2} = \frac{1}{10^2} = \frac{1}{100}$.
$\frac{1}{100}$. $10^{-2} = \frac{1}{10^2} = \frac{1}{100}$.
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