Question

`( (1)/(2) ) {}^( - 5)`express the following expression into non zero and non negative exponents.

Answer 1

32

Explanation:

The expression is given below as

`((1)/(2))^(-5)`

To solve this expression, we need to apply the law of indices

`x^(-1)\text{ = }\frac{1\text{ }}{x^{1^{}}}`

Let x = 1/2

`(x)^(-5)\text{ = }(1)/(x^5)`

substitute the value of x = 1/2 into the above-simplified expression

`\begin{gathered} ((1)/(2))^(-5)\text{ = }(1)/(((1)/(2))^5) \\ =\text{ }(1)/(((1)/(32))) \\ =\text{ }\frac{32\cdot\text{ 1}}{1} \\ =\text{ 32} \end{gathered}`

Hence, (1/2)^-5 is 32