Use the laws of exponents to simplify. Write the answer with positive exponents.
-$$\left( 5 a ^ { 1 / 7 } \cdot b ^ { 5 / 7 } \right) ^ { 3 }$$
A) $5 a ^ { 3 / 7 } b ^ { 15 / 7 }$
B) $125 ( a b ) ^ { 15 / 7 }$
C) $15 a ^ { 3 / 7 } b ^ { 5 / 7 }$
D) $125 a ^ { 3 / 7 } b ^ { 15 / 7 }$

Question

Quizplus · Accepted Answer

When raising a product to a power, you raise each factor in the product to that power. Here, $5^3 = 125$, $a^{(1/7) \cdot 3} = a^{3/7}$, and $b^{(5/7) \cdot 3} = b^{15/7}$.

Use the Laws of Exponents to Simplify (5a1/7⋅b5/7)3\left( 5 a ^ { 1 / 7 } \cdot b ^ { 5 / 7 } \right) ^ { 3 }(5a1/7⋅b5/7)3

Use the Laws of Exponents to Simplify $\left( 5 a ^ { 1 / 7 } \cdot b ^ { 5 / 7 } \right) ^ { 3 }$