Question

simplify rational exponents equation is 125 4/3

Answer 1

To simplify the expression \( 125^{4/3} \), we can break it down into steps:

1. First, rewrite \( 125 \) as a power of \( 5 \):
\[
125 = 5^3
\]

2. Now substitute \( 125 \) in the expression:
\[
125^{4/3} = (5^3)^{4/3}
\]

3. Use the power of a power property of exponents, which states that \( (a^m)^n = a^{mn} \):
\[
(5^3)^{4/3} = 5^{3 \cdot (4/3)}
\]

4. Multiply the exponents:
\[
3 \cdot (4/3) = 4
\]
So, we have:
\[
5^{4}
\]

5. Finally, calculate \( 5^4 \):
\[
5^4 = 625
\]

Thus, the simplified form of \( 125^{4/3} \) is:
\[
\boxed{625}
\]