What is the value of (5/4)−3

?(1 point)
Responses

64125
64 over 125

12564
125 over 64

−12564
negative 125 over 64

−64125
negative 64 over 125

1 answer

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 \( \frac{64}{125} \)).