8th Grade Math Flashcards: Apply Properties Of Integer Exponents

What this deck covers

This deck focuses on Apply Properties Of Integer Exponents, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the simplified form of $(4 \cdot 7)^2$?

Answer: $4^2 \cdot 7^2$. Using power of a product rule: $(4 \cdot 7)^2 = 4^2 \cdot 7^2$.

Flashcard 2: What is the value of $(3^2)^4$?

Answer: $3^8$. Power of a power: $(3^2)^4 = 3^{2 \cdot 4} = 3^8$.

Flashcard 3: What is the value of $\frac{5^9}{5^2}$?

Answer: $5^7$. Quotient rule: $\frac{5^9}{5^2} = 5^{9-2} = 5^7$.

Flashcard 4: State the power of a product rule for $(ab)^n$.

Answer: $(ab)^n = a^n b^n$. A power distributes over multiplication.

Flashcard 5: What is the value of $\left(\frac{4}{5}\right)^2$ written as a quotient of powers?

Answer: $\frac{4^2}{5^2}$. Power of a quotient: $(\frac{a}{b})^n = \frac{a^n}{b^n}$

Flashcard 6: State the product of powers rule for the same base $a^m \cdot a^n$.

Answer: $a^m \cdot a^n = a^{m+n}$. When multiplying powers with the same base, add the exponents.

Flashcard 7: What is the value of $2^3 \cdot 2^5$?

Answer: $2^8$. Product rule: $2^3 \cdot 2^5 = 2^{3+5} = 2^8$.

Flashcard 8: What is the value of $(-1)^{13}$?

Answer: $-1$. $(-1)$ to an odd power equals $-1$.

Flashcard 9: What is the value of $(-1)^{12}$?

Answer: $1$. $(-1)$ to an even power equals $1$.

Flashcard 10: What is the value of $1^{-5}$?

Answer: $1$. $1$ raised to any power equals $1$.

Flashcard 11: State the power of a quotient rule for $\left(\frac{a}{b}\right)^n$ where $b \ne 0$.

Answer: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$. A power distributes over division.

Flashcard 12: State the quotient of powers rule for the same base $\frac{a^m}{a^n}$ where $a \ne 0$.

Answer: $\frac{a^m}{a^n} = a^{m-n}$. When dividing powers with the same base, subtract the exponents.

Flashcard 13: State the power of a power rule for $(a^m)^n$.

Answer: $(a^m)^n = a^{mn}$. When raising a power to a power, multiply the exponents.

Flashcard 14: What is the value of $(2 \cdot 7)^3$ written as a product of powers?

Answer: $2^3 \cdot 7^3$. Power of a product: $(ab)^n = a^n b^n$.

Flashcard 15: What is the value of $3^2 \cdot 3^{-5}$ expressed with a positive exponent?

Answer: $\frac{1}{3^3}$. Product rule gives $3^{2+(-5)} = 3^{-3} = \frac{1}{3^3}$.

Flashcard 16: What is the value of $10^{-3}$ expressed as a fraction?

Answer: $\frac{1}{10^3}$. Negative exponent rule: $a^{-n} = \frac{1}{a^n}$.

Flashcard 17: What is the value of $\frac{2^{-4}}{2^{-1}}$ expressed with a positive exponent?

Answer: $\frac{1}{2^3}$. Quotient rule: $\frac{2^{-4}}{2^{-1}} = 2^{-4-(-1)} = 2^{-3} = \frac{1}{2^3}$.

Flashcard 18: Identify the equivalent expression for $\frac{a^7}{a^{10}}$ using integer exponent rules.

Answer: $a^{-3}$. Quotient rule: $\frac{a^7}{a^{10}} = a^{7-10} = a^{-3}$.

Flashcard 19: Find the simplified form of $\left(\frac{x^3 y^{-2}}{x^{-1}}\right)$ using exponent rules.

Answer: $x^4 y^{-2}$. Simplify: $\frac{x^3 y^{-2}}{x^{-1}} = x^{3-(-1)} y^{-2} = x^4 y^{-2}$.

Flashcard 20: State the negative exponent rule for $a^{-n}$ where $a \ne 0$ and $n$ is a positive integer.

Answer: $a^{-n} = \frac{1}{a^n}$. A negative exponent means reciprocal with positive exponent.

Flashcard 21: What is $(5^2)^3$ written as a single power of $5$?

Answer: $5^6$. Power of a power: $5^{2 \times 3} = 5^6$.

Flashcard 22: What is $\frac{2^7}{2^3}$ written as a single power of $2$?

Answer: $2^4$. Quotient rule: $2^{7-3} = 2^4$.

Flashcard 23: What is $\left(\frac{3}{5}\right)^2$ written as a fraction with exponents removed?

Answer: $\frac{9}{25}$. $\frac{3^2}{5^2} = \frac{9}{25}$.

Flashcard 24: What is the value of $a^0$ for $a \ne 0$?

Answer: $a^0 = 1$. Any nonzero number to the zero power equals 1.

Flashcard 25: What is the value of $3^2 \cdot 3^{-5}$ written as a single power of $3$?

Answer: $3^{-3}$. Product rule: $3^{2+(-5)} = 3^{-3}$.

Flashcard 26: What is the value of $3^{-3}$ written as a fraction in simplest form?

Answer: $\frac{1}{27}$. $3^{-3} = \frac{1}{3^3} = \frac{1}{27}$.

Flashcard 27: What is $(2 \cdot 3)^4$ written using powers of $2$ and $3$?

Answer: $2^4 \cdot 3^4$. Power of a product: distribute the exponent 4 to both factors.

Flashcard 28: State the negative exponent rule for $a^{-n}$ where $a \ne 0$ and $n$ is an integer.

Answer: $a^{-n} = \frac{1}{a^n}$. A negative exponent means reciprocal with positive exponent.

Flashcard 29: What is the value of $\frac{a^m}{a^m}$ for $a \ne 0$?

Answer: $\frac{a^m}{a^m} = 1$. Any nonzero expression divided by itself equals 1.

Flashcard 30: What is $10^{-2}$ written as a fraction in simplest form?

Answer: $\frac{1}{100}$. $10^{-2} = \frac{1}{10^2} = \frac{1}{100}$.