Question

use the properties of exponents to rewrite the expression. $(g^{2}h^{3})^{6}$
a. $g^{1}2h^{3}$
b. $g^{8}h^{9}$
c. $g^{8}h^{18}$
d. $g^{12}h^{18}$
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Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((g^{2}h^{3})^{6}\), we can apply this rule to get \( (g^{2})^{6}(h^{3})^{6} \).

Step2: Apply power of a power rule

The power of a power rule states that \((a^m)^n = a^{m \times n}\). Applying this to \( (g^{2})^{6} \), we have \( g^{2\times6}=g^{12} \). Applying it to \( (h^{3})^{6} \), we have \( h^{3\times6}=h^{18} \).

Step3: Combine the results

Combining the results from Step 2, we get \( g^{12}h^{18} \).

Answer:

D. \( g^{12}h^{18} \)