Question

current objective
use the laws of exponents to simplify expression

question
simplify: \\((a^{-8}b^{4}c^{6})^{\frac{1}{2}}\\).

provide your answer below:

Explanation:

Apply the power of a product rule

$$ (a^{-8}b^4c^6)^{\frac{1}{2}} = (a^{-8})^{\frac{1}{2}} \cdot (b^4)^{\frac{1}{2}} \cdot (c^6)^{\frac{1}{2}} $$

Multiply exponents

$$ a^{-8 \cdot \frac{1}{2}} b^{4 \cdot \frac{1}{2}} c^{6 \cdot \frac{1}{2}} = a^{-4} b^2 c^3 $$

Rewrite with positive exponents

$$ \frac{b^2 c^3}{a^4} $$

Answer:

Simplify: \((a^{-8}b^4c^6)^{\frac{1}{2}}\).

Provide your answer below:
<blank>\(\frac{b^2c^3}{a^4}\)</blank>