Question

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

Answer 1

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:

Bhai it is incorrect answer