What is the value of (5/4)−3

Question

?(1 point)
Responses

64125
64 over 125

12564
125 over 64

−12564
negative 125 over 64

−64125
negative 64 over 125

Answer 1

To evaluate ${\left(\frac{5}{4}\right)}^{-3}$, we can use the property of exponents that states $a^{-n}=\frac{1}{a^n}$. Thus, we have:

$${\left(\frac{5}{4}\right)}^{-3}=\frac{1}{{\left(\frac{5}{4}\right)}^3}$$

Next, we calculate ${\left(\frac{5}{4}\right)}^3$:

$${\left(\frac{5}{4}\right)}^3=\frac{5^3}{4^3}=\frac{125}{64}$$

Now we can substitute this back into our equation:

$${\left(\frac{5}{4}\right)}^{-3}=\frac{1}{\frac{125}{64}}=\frac{64}{125}$$

Thus, the value of ${\left(\frac{5}{4}\right)}^{-3}$ is $\frac{64}{125}$.

Therefore, the correct response is:

64 over 125 (or $\frac{64}{125}$).