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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 7: Q2. (page 466)

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
Simplify the following expression.
${(\frac{2 w^{2} z^{5}}{3 y^{4}})}^{3}$
F $\frac{2 w^{5} z^{8}}{3 y^{7}}$
G $\frac{8 w^{6} z^{15}}{27 y^{12}}$
H $\frac{8 w^{5} z^{8}}{27 y^{7}}$
J $\frac{2 w^{6} z^{15}}{3 y^{12}}$

Short Answer

Expert verified

The value of the given expression ${(\frac{2 w^{2} z^{5}}{3 y^{4}})}^{3}$ is $\frac{8 w^{6} z^{15}}{27 y^{12}}$ . Therefore, the option G is correct.

Step by step solution

01

Step 1. Write the property of power of a product, power of a quotient and power of a power.

The property of power of a product states that:

${(a b)}^{m} = a^{m} b^{m}$

The property of power of a quotient states that:

${(\frac{a}{b})}^{m} = \frac{a^{m}}{b^{m}}$

The property of power of a power states that:

${(a^{m})}^{n} = a^{m n}$

02

Step 2. Simplify the given expression.

The value of the given expression ${(\frac{2 w^{2} z^{5}}{3 y^{4}})}^{3}$ after simplification is:

role="math" localid="1647682531721" ${(\frac{2 w^{2} z^{5}}{3 y^{4}})}^{3} = \frac{{(2 w^{2} z^{5})}^{3}}{{(3 y^{4})}^{3}} (powerofaquotient) = \frac{2^{3} {(w^{2})}^{3} {(z^{5})}^{3}}{3^{3} {(y^{4})}^{3}} (powerofaproduct) = \frac{8 w^{2 脳 3} z^{5 脳 3}}{27 y^{4 脳 3}} (powerofapower)$

Therefore, the value of the given expression ${(\frac{2 w^{2} z^{5}}{3 y^{4}})}^{3}$ is $\frac{8 w^{6} z^{15}}{27 y^{12}}$ . Therefore, the option G is correct.

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