Question

What is the value of (5 over 4)^−3
?(1 point)
Responses

64125
64 over 125

12564
125 over 64

−12564
negative 125 over 64

−64 over 125

Answer 1

To calculate \((\frac{5}{4})^{-3}\), we can use the property of exponents that states \(a^{-n} = \frac{1}{a^n}\).

So, 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, substituting this back, we find:

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

Therefore, the value of \((\frac{5}{4})^{-3}\) is:

\[
\frac{64}{125}
\]

Thus, the correct response is:

**64 over 125**.