which expression is equivalent to $\frac{5y^{3}}{(5y)^{-2}}$?\n$y^{5}$\n$y^{6}$\n$125y^{3}$\n$125y^{5}$

Explanation:

Step1: Apply negative - exponent rule

Recall that (a^{-n}=\frac{1}{a^{n}}). So, ((5y)^{-2}=\frac{1}{(5y)^{2}}), and the original expression (\frac{5y^{3}}{(5y)^{-2}}) becomes (5y^{3}\times(5y)^{2}).

Step2: Expand ((5y)^{2})

Using the power - of - a - product rule ((ab)^{n}=a^{n}b^{n}), we have ((5y)^{2}=5^{2}y^{2}=25y^{2}). Then the expression is (5y^{3}\times25y^{2}).

Step3: Multiply the coefficients and add the exponents of (y)

Multiply the coefficients (5\times25 = 125), and for the variables with the same base (y), use the rule (a^{m}\times a^{n}=a^{m + n}), so (y^{3}\times y^{2}=y^{3 + 2}=y^{5}). The result is (125y^{5}).

Answer:

(125y^{5})