Question

question 20 (mandatory) (1 point)
write (3/4)^(-3) as a fraction or integer without using exponents.

a) 64/27
b) -27/64
c) 1
d) 27/64

Explanation:

Step1: Apply negative - exponent rule

By the rule $a^{-n}=\frac{1}{a^{n}}$, for $(\frac{3}{4})^{-3}$, we have $(\frac{3}{4})^{-3}=\frac{1}{(\frac{3}{4})^{3}}$.

Step2: Calculate $(\frac{3}{4})^{3}$

$(\frac{3}{4})^{3}=\frac{3^{3}}{4^{3}}=\frac{27}{64}$ according to the power - of - a - fraction rule $( \frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}$.

Step3: Find the final result

Since $(\frac{3}{4})^{-3}=\frac{1}{(\frac{3}{4})^{3}}$ and $(\frac{3}{4})^{3}=\frac{27}{64}$, then $(\frac{3}{4})^{-3}=\frac{64}{27}$.

Answer:

A. $\frac{64}{27}$