which expression is equivalent to $\frac{(2g^{5})^{3}}{(4h^{2})^{3}}$?\n$\frac{g^{15}}{8h^{6}}$\n$\frac{g^{5}…

which expression is equivalent to $\frac{(2g^{5})^{3}}{(4h^{2})^{3}}$?\n$\frac{g^{15}}{8h^{6}}$\n$\frac{g^{5}}{2h^{2}}$\n$\frac{g^{15}}{2h^{6}}$\n$\frac{g^{8}}{8h^{5}}$

which expression is equivalent to $\frac{(2g^{5})^{3}}{(4h^{2})^{3}}$?\n$\frac{g^{15}}{8h^{6}}$\n$\frac{g^{5}}{2h^{2}}$\n$\frac{g^{15}}{2h^{6}}$\n$\frac{g^{8}}{8h^{5}}$

Answer

Explanation:

Step1: Apply power - of - a - product rule

For ((ab)^n=a^n\times b^n), ((2g^{5})^{3}=2^{3}\times(g^{5})^{3}) and ((4h^{2})^{3}=4^{3}\times(h^{2})^{3}). So the expression (\frac{(2g^{5})^{3}}{(4h^{2})^{3}}) becomes (\frac{2^{3}\times(g^{5})^{3}}{4^{3}\times(h^{2})^{3}}).

Step2: Calculate powers of coefficients and apply power - of - a - power rule

(2^{3}=8), (4^{3}=64), and by ((a^{m})^{n}=a^{mn}), ((g^{5})^{3}=g^{15}), ((h^{2})^{3}=h^{6}). The expression is (\frac{8g^{15}}{64h^{6}}).

Step3: Simplify the coefficient

(\frac{8}{64}=\frac{1}{8}), so the simplified expression is (\frac{g^{15}}{8h^{6}}).

Answer:

(\frac{g^{15}}{8h^{6}})