What is the value of (54)−3

Question

?(1 point)
Responses

−12564
negative 125 over 64

12564
125 over 64

−64125
negative 64 over 125

64125

Answer 1

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

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

Now, we need to calculate \( (54)^3 \):

\[ 54^3 = 54 \times 54 \times 54 = 157464 \]

Thus,

\[ (54)^{-3} = \frac{1}{157464} \]

Now, we can simplify this fraction:

\(\frac{1}{157464}\) corresponds to a numerical value but does not directly match any of the options given. However, if it were to be expressed as a fraction in terms of smaller numbers, we can explore potential options.

Looking at the options provided, we notice:

• \(-\frac{125}{64}\)
• \(\frac{125}{64}\)
• \(-\frac{64}{125}\)
• \(64125\)

None of these seem applicable based solely on the calculation above.

Therefore, considering common mathematical operations and conversions, it appears that a related misunderstanding or misinterpretation of notation could have occurred if we seek the value. If the phrasing of the options or intention was to find a reciprocal function within a different base, we would apply that to another existing choice.

For the calculated outcome of \((54)^{-3}\):

\[ \approx 0.00000635 \]

Is not found superficially in any of the responses; please double-check the context or if a clarification is provided for proper input and retracement of the original input equation if something fundamental might be overlooked. The answer in standard notation as outlined is \( \frac{1}{(54)^3} \) but does not align with available selections. If evaluating more, conclusions on fractions should highlight exact divisions of 1 for evaluation close to fractions outside whole squared powers or bases of 54 themselves hence items lead to - misunderstanding or oversight when reviewing fractions beyond base states.

For computational alignment, verifying the origin would aid smooth-calculated knowledge towards fraction deployment as necessary. Please adjust questions if requiring further assistance around element and numeric fractions and automated outcomes!

Answer 2

whats the answer

Answer 3

To find the value of \((54)^{-3}\):

1. Convert the negative exponent: \[ (54)^{-3} = \frac{1}{(54)^3} \]

2. Calculate \( (54)^3 \): \[ 54^3 = 54 \times 54 \times 54 = 157464 \]

3. Now, substitute back into the fraction: \[ (54)^{-3} = \frac{1}{157464} \]

This doesn't seem to match the original options directly. However, if you're looking for a fraction in a simplified or negative form:

The appropriate representation from what's provided appears to be closest in context of negatives toward reciprocal fractions in their bases, as \( \frac{1}{54^3} \). It's crucial to recognize that none of these options properly represent \( (54)^{-3} \) as calculated.

If we must match to an exact listed response:

\[ = \frac{1}{157464} \]

But if we misunderstood the numerical presentation, in terms of presented negatives or fractions in simpler correspondences:

The listed responses are:

• \(-\frac{125}{64}\)
• \(\frac{125}{64}\)
• \(-\frac{64}{125}\)
• \(64125\)

Given the outcomes explored, none equal to \(\frac{1}{157464}\) or transformed states near existing fractions. If operational intent reflects towards refactoring of possible power negatives, please clarify or restate the goal required around outcomes and numeric cores as well!

Conclusively, for direct values common outside specifics is None of the given options apply for exact computation representing \( (54)^{-3} = \frac{1}{157464} \).

Answer 4

whats the closest answer

Answer 5

To represent \((54)^{-3}\) in the context of the provided choices, we calculated:

\[ (54)^{-3} = \frac{1}{(54)^3} = \frac{1}{157464} \]

While \(\frac{1}{157464}\) does not directly match any listed choice, we can look for an approximate relationship or value.

Let’s analyze the provided options:

• \(-\frac{125}{64}\)
• \(\frac{125}{64}\)
• \(-\frac{64}{125}\)
• \(64125\)

However, if we examine \(\frac{125}{64}\) and \(-\frac{64}{125}\):

1. The decimal for \(-\frac{64}{125} \approx -0.512\)
2. The decimal for \(\frac{125}{64} \approx 1.953125\)

Both are significantly different from the calculated \((54)^{-3}\).

In terms of magnitude, as \((54)^{-3}\) yields a very small positive decimal approximately equal to \(0.00000635\), it does not closely align with any of the negative values.

Considering closest fractions in magnitude:

1. Among all options, the fraction \(-\frac{64}{125}\) reveals its absolute value approaching a response footing around lower number value representations, more so if assigning lower values to the full numeric square.

2. This suggests nominal significance in comparing against larger numbers as downward states approach the vectors via re-positioning.

So if forced to pick the closest option, that would likely be just \(-\frac{64}{125}\).

Thus, while not a direct match, it’s the nearest selection to consideration if constructive choice based on highlighting fractions or negative alignments is performed.

Final Closest Answer: \(-\frac{64}{125}\)