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Answer :
To evaluate [tex]\(-\left(5^{-4}\right)\left(5^2\right)\)[/tex], we can break down the problem into several steps:
1. Calculate [tex]\(5^{-4}\)[/tex]:
- The expression [tex]\(5^{-4}\)[/tex] means [tex]\( \frac{1}{5^4} \)[/tex].
- [tex]\(5^4 = 5 \times 5 \times 5 \times 5 = 625\)[/tex].
- So, [tex]\(5^{-4} = \frac{1}{625} = 0.0016\)[/tex].
2. Calculate [tex]\(5^2\)[/tex]:
- The expression [tex]\(5^2\)[/tex] means [tex]\(5 \times 5\)[/tex].
- Therefore, [tex]\(5^2 = 25\)[/tex].
3. Multiply the results:
- We now need to multiply [tex]\(0.0016\)[/tex] and [tex]\(25\)[/tex].
- [tex]\(0.0016 \times 25 = 0.04\)[/tex].
4. Apply the negative sign:
- We need to negate the result from the multiplication.
- [tex]\(-0.04\)[/tex].
So, the evaluated result of [tex]\(-\left(5^{-4}\right)\left(5^2\right)\)[/tex] is [tex]\(-0.04\)[/tex].
Therefore, the correct choice from the given options is not directly listed. However, our steps show that:
- The correct answer does exist and is accurately calculated as [tex]\(-0.04\)[/tex].
None of the given options (A, B, C, D) match this calculated value exactly, but our result follows logically from the calculations shown.
1. Calculate [tex]\(5^{-4}\)[/tex]:
- The expression [tex]\(5^{-4}\)[/tex] means [tex]\( \frac{1}{5^4} \)[/tex].
- [tex]\(5^4 = 5 \times 5 \times 5 \times 5 = 625\)[/tex].
- So, [tex]\(5^{-4} = \frac{1}{625} = 0.0016\)[/tex].
2. Calculate [tex]\(5^2\)[/tex]:
- The expression [tex]\(5^2\)[/tex] means [tex]\(5 \times 5\)[/tex].
- Therefore, [tex]\(5^2 = 25\)[/tex].
3. Multiply the results:
- We now need to multiply [tex]\(0.0016\)[/tex] and [tex]\(25\)[/tex].
- [tex]\(0.0016 \times 25 = 0.04\)[/tex].
4. Apply the negative sign:
- We need to negate the result from the multiplication.
- [tex]\(-0.04\)[/tex].
So, the evaluated result of [tex]\(-\left(5^{-4}\right)\left(5^2\right)\)[/tex] is [tex]\(-0.04\)[/tex].
Therefore, the correct choice from the given options is not directly listed. However, our steps show that:
- The correct answer does exist and is accurately calculated as [tex]\(-0.04\)[/tex].
None of the given options (A, B, C, D) match this calculated value exactly, but our result follows logically from the calculations shown.
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