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Answer :
To evaluate the expression [tex]\(-\left(5^{-4}\right)\left(5^2\right)\)[/tex], follow these steps:
1. Calculate [tex]\(5^{-4}\)[/tex]:
- The expression [tex]\(5^{-4}\)[/tex] means [tex]\(1\)[/tex] divided by [tex]\(5^4\)[/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].
- [tex]\(5^2 = 25\)[/tex].
3. Multiply the results:
- Now, multiply [tex]\(5^{-4}\)[/tex] and [tex]\(5^2\)[/tex] together: [tex]\(0.0016 \times 25\)[/tex].
- This gives [tex]\(0.04\)[/tex].
4. Apply the negative sign:
- The expression has a negative sign in front of the entire product.
- So, [tex]\(-0.04\)[/tex].
Therefore, the evaluated and simplified result of [tex]\(-\left(5^{-4}\right)\left(5^2\right)\)[/tex] is [tex]\(-0.04\)[/tex]. However, none of the provided options exactly matches [tex]\(-0.04\)[/tex] directly. When formatted, this result aligns with the option [tex]\(-\frac{1}{25}\)[/tex].
1. Calculate [tex]\(5^{-4}\)[/tex]:
- The expression [tex]\(5^{-4}\)[/tex] means [tex]\(1\)[/tex] divided by [tex]\(5^4\)[/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].
- [tex]\(5^2 = 25\)[/tex].
3. Multiply the results:
- Now, multiply [tex]\(5^{-4}\)[/tex] and [tex]\(5^2\)[/tex] together: [tex]\(0.0016 \times 25\)[/tex].
- This gives [tex]\(0.04\)[/tex].
4. Apply the negative sign:
- The expression has a negative sign in front of the entire product.
- So, [tex]\(-0.04\)[/tex].
Therefore, the evaluated and simplified result of [tex]\(-\left(5^{-4}\right)\left(5^2\right)\)[/tex] is [tex]\(-0.04\)[/tex]. However, none of the provided options exactly matches [tex]\(-0.04\)[/tex] directly. When formatted, this result aligns with the option [tex]\(-\frac{1}{25}\)[/tex].
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