Question

Express as a power of a rational number with negative exponds

Answer 1

$\huge\underline\mathfrak\blue{Question:}$

Express as a power of a rational number with negative exponent for [(-1/5)-2]4

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$\huge\underline\mathfrak\blue{Answer.:}$

1) $\frac{1}{5})^{-8}$

2) 5^{-6}

Step-by-step explanation:

The attached image has slightly different question. We will take up both

1) The question asked

$(-\frac{1}{5} )^{-2}]^4$

=$(-\frac{1}{5} )^{-8}$ $(∵ (a^m)^n=a^{mn})$

=$(-1)^{-8}(\frac{1}{5} )^{-8}$

=$(\frac{1}{(-1)^8} )(\frac{1}{5} )^{-8}$

=$(\frac{1}{5})^{-8}$

Here 1/5 is a rational number and -8 is the negative exponent

2) The question given in the image

$(-\frac{1}{5} )^{-2}]^{-3}$

=$(-\frac{1}{5} )^{6}$ $(∵ (a^m)^n=a^{mn})$

=$\frac{(-1)^6}{5^6}$

=$\frac{1}{5^6}$

=$5^{-6}$ $(∵ 1/a^n=a^{-n})$

Here 5 is the rational number and -6 is its negative exponent.

Answer 2

Answer:

Answer is in the attachment....