Question

Use the rules of exponents to simplify the expressions. Match the expression with its equivalent value.

Answer 1

Answer/Step-by-step explanation:

1.
`((-2)^(-5))/((-2)^(-10))`

Apply the Quotient rule: i.e.
`(x^n)/(x^m) = x^(n - m)`

`= (-2)^(-5 - (-10)) = (-2)^5} = -32`

2.
`2^(-1) * 2^(-4)`

Apply the product rule: i.e.
`x^n * x^m = x^(n + m)`.

`= 2^(-1 + (-4)) = 2^(-1 - 4)`

`= 2^(-5)`

Apply the negative exponent rule: i.e.
`x^(-n) = (1)/(x^n)`

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

`= (1)/(32)`

3.
`(-(1)/(2))^3 * (-(1)/(2))^2`

Apply product rule

`= (-(1)/(2))^(3 + 2)`

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

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

`= -(1)/(32)`

4.
`(2)/(2^(-4))`

Apply the rules of 1 and quotient rule

`= 2^(1 - (-4))`

`= 2^(1 + 4)`

`= 2^(5) = 32`