Question

What is the value of%C2%A0 (54)−3 ?(1 point) Responses −12564 negative 125 over 64 64125 64 over 125 12564 125 over 64 −64125

Answer 1

To calculate \( (54)^{-3} \), we first rewrite it using the property of negative exponents:

\[
(54)^{-3} = \frac{1}{(54)^3}
\]

Next, we need to compute \( (54)^3 \):

\[
54^3 = 54 \times 54 \times 54
\]
Calculating this step-by-step:

1. \( 54 \times 54 = 2916 \)
2. Now, multiply that result by 54:
\[
2916 \times 54
\]
- First, we'll break it down:
\[
2916 \times 50 + 2916 \times 4
\]
- Calculate \( 2916 \times 50 \):
\[
2916 \times 50 = 145800
\]
- Now calculate \( 2916 \times 4 \):
\[
2916 \times 4 = 11664
\]
- Now, add these two results together:
\[
145800 + 11664 = 157464
\]
Thus, \( 54^3 = 157464 \).

Putting it all together for \( (54)^{-3} \):
\[
(54)^{-3} = \frac{1}{157464}
\]

To find a simpler fraction, we can write this value as a decimal:
\[
\frac{1}{157464} \approx 0.00000635
\]
or in a fraction form, it remains \( \frac{1}{54^3} \) or simply \( \frac{1}{157464} \).

However, this result does not match the options you provided. The closest interpretation, if we also consider something like \( 64/125 \) or \( -64/125 \), could be incorrect options.

Since none of your provided options \( \text{−12564, 125 over 64, 64125, 64 over 125, 12564, 125 over 64, -64125} \) appear mathematically corresponding to \( (54)^{-3}\), please review any further or provide additional context for clarification.

If the actual question was to compute \( (54/64)^{-3} \) or similar, please clarify for exact computation.