To simplify \( 32^{4/5} \), we can break it down into steps: 1. Rewrite \( 32 \) as a power of 2: \[ 32 = 2^5 \] Thus, we can write: \[ 32^{4/5} = (2^5)^{4/5} \] 2. Apply the exponent rule \((a^m)^n = a^{m \cdot n}\): \[ (2^5)^{4/5} = 2^{5 \cdot \frac{4}{5}} = 2^4 \] 3. Calculate \( 2^4 \): \[ 2^4 = 16 \] Therefore, the simplified form of \( 32^{4/5} \) is \( \boxed{16} \).

Simplify.

32^4/5

1 answer

To simplify \( 32^{4/5} \), we can break it down into steps:

Rewrite \( 32 \) as a power of 2: \[ 32 = 2^5 \] Thus, we can write: \[ 32^{4/5} = (2^5)^{4/5} \]
Apply the exponent rule \((a^m)^n = a^{m \cdot n}\): \[ (2^5)^{4/5} = 2^{5 \cdot \frac{4}{5}} = 2^4 \]
Calculate \( 2^4 \): \[ 2^4 = 16 \]

Therefore, the simplified form of \( 32^{4/5} \) is \( \boxed{16} \).