Question

which expression is equivalent to the given expression? (6n^{-5})(3n^{-3})^2
a. $\frac{36}{n^{11}}$
b. $54n^{30}$
c. $36n^{30}$
d. $\frac{54}{n^{11}}$

Explanation:

Step1: Expand $(3n^{-3})^2$

Using the power - of - a - product rule $(ab)^m=a^m b^m$ and power - of - a - power rule $(a^m)^n=a^{mn}$, we have $(3n^{-3})^2 = 3^2\times(n^{-3})^2=9n^{-6}$.

Step2: Multiply $(6n^{-5})$ and $9n^{-6}$

Using the product rule of exponents $a^m\times a^n=a^{m + n}$ and multiplying the coefficients, we get $(6n^{-5})\times(9n^{-6})=(6\times9)n^{-5+( - 6)} = 54n^{-11}=\frac{54}{n^{11}}$.

Answer:

D. $\frac{54}{n^{11}}$