Question

select the equivalent expression.
\\(\left(\frac{a}{b^{3}}\
ight)^{4}=?\\)
choose 1 answer:
\\(\textcircled{a}\\) \\(\frac{a^{5}}{b^{7}}\\)
\\(\textcircled{b}\\) \\(\frac{a}{b^{81}}\\)
\\(\textcircled{c}\\) \\(\frac{a^{8}}{b^{8}}\\)
\\(\textcircled{d}\\) \\(\frac{a^{4}}{b^{12}}\\)

Explanation:

Step1: Apply power - of - a - quotient rule

$(\frac{a}{b^3})^4=\frac{a^4}{(b^3)^4}$

Step2: Apply power - of - a - power rule

$(b^3)^4 = b^{3\times4}=b^{12}$
So $(\frac{a}{b^3})^4=\frac{a^4}{b^{12}}$

Answer:

D. $\frac{a^{4}}{b^{12}}$