Algebra II - Distributing Exponents (Power Rule)

Simplify:

$\frac{(x^2y^3)^9}{xy^7}$

$x^{17}y^{20}$

$x^{10}y^5$

$\frac{x^9}{y^{36}}$

$x^{11}y^{27}$

Explanation

Recall that when an exponent is raised to another exponent, you will need to multiply the two exponents together.

Start by simplifying the numerator:

$(x^2y^3)^9=x^{18}y^{27}$

Now, place this on top of the denominator and simplify. Recall that when you divide exponents that have the same base, you will subtract the exponent in the denominator from the exponent in the numerator.

$\frac{x^{18}y^{27}}{xy^7}=x^{17}y^{20}$

Evaluate:

$x^{35}$

$x^{12}$

$x^{24}$

$x^{57}$

$x^{36}$

Explanation

When an exponent is being raised by another exponent, we just multiply the powers and keep the base the same.

$(x^5)^7=x^{5&*7}=x^{35}$

Solve: $2(27)^{\frac{4}{3}}$

$162\sqrt[3]{2}$

$81\sqrt{2}$

Explanation

First convert into a known base. The number can be rewritten as .

Rewrite the expression.

$2(27)^{\frac{4}{3}}=2(3^3)^{\frac{4}{3}}$

Use the power rule to multiply the exponents.

$2(3^3)^{\frac{4}{3}} = 2(3)^4$

Use order of operations to evaluate the expression.

$2(3)^4 = 2(3\cdot 3 \cdot 3\cdot 3) = 2(81)= 162$

Simplify:

$(-2x^{-2}y^3)^{3}$

$\frac{-8y^9}{x^6}$

$\frac{8y^9}{x^6}$

$\frac{-8y^9}{x^3}$

$\frac{y^9}{x^6}$

$\frac{-8y^5}{x^6}$

Explanation

The power that's outside of the parentheses needs to be distributed to every term inside the parentheses:

$-2^3x^{-2\cdot 3}y^{3\cdot 3}$ .

When there's a power outside the parentheses, the exponents are multiplied:

$-8x^{-6}y^9$ .

To get rid of the negative exponent, put it on the denominator:

$\frac{-8y^9}{x^6}$ .

Simplify: $[(2^{-3})^{-2}]^{-\frac{1}{2}}$

$\frac{1}{8}$

$\frac{1}{64}$

$\frac{1}{32}$

Explanation

We can use the power rule of exponents to simplify this expression.

$(x^{Y})^Z =x^{YZ}$

$[(2^{-3})^{-2}]^{-\frac{1}{2}} = 2^{(-3)\cdot (-2 )\cdot( -\frac{1}{2})}$

The expression becomes:

$2^{-3}$

We can rewrite this as a fraction.

$2^{-3} = \frac{1}{2^3}=\frac{1}{8}$

The answer is: $\frac{1}{8}$

Evaluate:

$\textup{The answer is not given.}$

Explanation

In order to evaluate this expression, we can use the distributive property of exponents to simplify.

Multiply the powers together.

$2(2^2)^4 = 2(2)^{2(4)} = 2(2^8)$

This is also the same as: $2^1 \cdot 2^8 = 2^{1+8} = 2^9$

$2^9 = (2\cdot2\cdot2)^3 = 8^3 =512$

The answer is:

Simplify: $(3^{600})^3$

$3^{1800}$

$27^{1800}$

$9^{1800}$

$3^{603}$

$27^{603}$

Explanation

The exponents are separated by a parentheses.

According to the distributive property of exponents, we can simply multiply the two exponents.

$3^{600\times 3} = 3^{1800}$

Do not cube the three!

The answer is: $3^{1800}$

Simplify: $(9\cdot3^{12})^5$

$3^{70}$

$9^{50}$

$3^{80}$

$3^{120}$

$9^{60}$

Explanation

In order to simplify this, we will first need to simplify the inner term of the parentheses.

Rewrite the nine with base three.

The expression becomes:

$(3^2\cdot3^{12})^5$

Since the common bases of a certain power are multiplied, the exponents can be added.

$(3^2\cdot3^{12})^5=(3^{2+12})^5 = (3^{14})^5$

Now that we have an exponent outside of a quantity, we can multiply the exponents together.

$(3^{14})^5 = 3^{70}$

The answer is: $3^{70}$

Simplify: $(x^4)^{-2}$

$x^{-8}$

$x^{-6}$

$x^{-2}$

Explanation

When an exponent is being raised by another exponent, we just multiply the powers and keep the base the same.

$(x^4)^{-2}=x^{4*-2}=x^{-8}$

Solve: $(8^{4})^{15}$

$8^{60}$

$8^{19}$

$2^{60}$

$2^{170}$

$4^{80}$

Explanation

Use the power rule of exponents to simplify this expression.

$(x^{Y})^Z = x^{YZ}$

Follow this rule to simplify the exponents.

$(8^{4})^{15} = 8^{4\times 15} = 8^{60}$

The answer is: $8^{60}$

Distributing Exponents (Power Rule)

Help Questions

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation