Question

1. simplify $(g^4h)^6$.

$\bigcirc$ $g^{10}h$
$\bigcirc$ $(g^{10}h)^6$
$\bigcirc$ $g^{24}h^6$
$\bigcirc$ $g^{24}h$

Explanation:

Step1: Apply power of a product rule

$(ab)^n = a^n b^n$, so $(g^4h)^6 = (g^4)^6 \cdot h^6$

Step2: Apply power of a power rule

$(a^m)^n = a^{m \cdot n}$, so $(g^4)^6 = g^{4 \times 6} = g^{24}$

Step3: Combine simplified terms

$g^{24} \cdot h^6 = g^{24}h^6$

Answer:

$\boldsymbol{g^{24}h^6}$ (the third option)