Simplify the expression. $\left( 625 y ^ { 4 } \right) ^ { 1 / 4 }$
A) $\quad 5 | y |$
B) $\quad 25 | y |$
C) $\quad 5 \left| y ^ { 2 } \right|$
D) $5 y$
E) $\quad 5 y ^ { 2 }$

Question

Quizplus · Accepted Answer

We can simplify the expression by using the fourth root property: $\left( a^b \right)^{1/b} = a$, where $a$ and $b$ are positive real numbers. Applying this property, we get:

$$\left( 625 y ^ { 4 } \right) ^ { 1 / 4 } = 625^{1/4} \cdot (y^4)^{1/4} = 5 \cdot \left| y \right| $$

Since $y$ can be positive or negative, we take the absolute value of $y$, which means the correct answer is A) 5 | y |.

Simplify the Expression (625y4)1/4\left( 625 y ^ { 4 } \right) ^ { 1 / 4 }(625y4)1/4

Simplify the Expression $\left( 625 y ^ { 4 } \right) ^ { 1 / 4 }$