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

1 = A

2= D

3= B

4= C

Answer/Step-by-step explanation:

1. [tex]\frac{(-2)^{-5}}{(-2)^{-10}}[/tex]

Apply the Quotient rule: i.e. [tex]\frac{x^n}{x^m} = x^{n - m}[/tex]

[tex]= (-2)^{-5 - (-10)} = (-2)^5} = -32[/tex]

2. [tex]2^{-1} * 2^{-4}[/tex]

Apply the product rule: i.e. [tex]x^n * x^m = x^{n + m}[/tex].

[tex]= 2^{-1 + (-4)} = 2^{-1 - 4}[/tex]

[tex]= 2^{-5}[/tex]

Apply the negative exponent rule: i.e. [tex]x^{-n} = \frac{1}{x^n}[/tex]

[tex]= 2^{-5} = \frac{1}{2^5}[/tex]

[tex]= \frac{1}{32}[/tex]

3. [tex](-\frac{1}{2})^3 * (-\frac{1}{2})^2[/tex]

Apply product rule

[tex]= (-\frac{1}{2})^{3 + 2}[/tex]

[tex]= (-\frac{1}{2})^{5}[/tex]

[tex]= -\frac{1^5}{2^5}[/tex]

[tex]= -\frac{1}{32}[/tex]

4. [tex]\frac{2}{2^{-4}}[/tex]

Apply the rules of 1 and quotient rule

[tex]= 2^{1 - (-4)}[/tex]

[tex]= 2^{1 + 4}[/tex]

[tex]= 2^{5} = 32[/tex]