Question

Q no 1 on attached photo

Answer 1

refer to the attachment for your answer.

laws of exponents used :-

• a^-b = (1/b)^b

• √(a)^b = b√a

Answer 2

Answer:

$\mathrm{Simplify}\:\sqrt{\left(81\right)^{-2}}:\quad \dfrac{1}{81}\quad \left(\mathrm{Decimal:\quad }\:0.01235\dots \right)$

Step-by-step explanation:

$\sqrt{\left(81\right)^{-2}}$

$\sqrt{a}=a^{\dfrac{1}{2}}$

$=\left(81^{-2}\right)^{\dfrac{1}{2}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}$

$=81^{\left(-2\right)\dfrac{1}{2}}$

$\left(-2\right)\dfrac{1}{2}$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$=-2\cdot \dfrac{1}{2}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \dfrac{b}{c}=\dfrac{a\:\cdot \:b}{c}$

$=-\dfrac{1\cdot \:2}{2}$

$\mathrm{Cancel\:the\:common\:factor:}\:2$

$=-1$

$=81^{-1}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\dfrac{1}{a}$

$=\dfrac{1}{81}$