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. $\frac{(-2)^{-5}}{(-2)^{-10}}$

Apply the Quotient rule: i.e. $\frac{x^n}{x^m} = x^{n - m}$

$= (-2)^{-5 - (-10)} = (-2)^5} = -32$

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. $x^{-n} = \frac{1}{x^n}$

$= 2^{-5} = \frac{1}{2^5}$

$= \frac{1}{32}$

3. $(-\frac{1}{2})^3 * (-\frac{1}{2})^2$

Apply product rule

$= (-\frac{1}{2})^{3 + 2}$

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

$= -\frac{1^5}{2^5}$

$= -\frac{1}{32}$

4. $\frac{2}{2^{-4}}$

Apply the rules of 1 and quotient rule

$= 2^{1 - (-4)}$

$= 2^{1 + 4}$

$= 2^{5} = 32$