Apply the properties of integer exponents to identify all of the expressions equivalent to 1/8. A. 2^-3 B. 2^3 C. 1/2^3 D. 2^2 x 2^-5 E. 2^-2 x 2^5
Accepted Solution
A:
Answer:The answers are A , C , DStep-by-step explanation:Lets revise the rule of exponent* [tex]a^{n}*a^{m}=a^{m+n}[/tex]* [tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]* [tex]\frac{1}{a^{-m}}=a^{m}[/tex]* [tex](\frac{a}{b})^{-m}=(\frac{b}{b})^{m}[/tex]Now lets solve the problemWe need all the expressions equivalent to [tex]\frac{1}{8}[/tex]A.∵ [tex]2^{-3}=\frac{1}{2^{3}}[/tex]∵ 2³ = 8∴ [tex]2^{-3}=\frac{1}{8}[/tex]Answer A is equivalent to [tex]\frac{1}{8}[/tex]B.∵ 2³ = 8Answer B is not equivalent to [tex]\frac{1}{8}[/tex]C.∵ 2³ = 8∴ [tex]\frac{1}{2^{3}}=\frac{1}{8}[/tex]Answer C is equivalent to [tex]\frac{1}{8}[/tex]D.∵ [tex]2^{2}*2^{-5}=2^{2+-5}=2^{-3}[/tex]∵ [tex]2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}[/tex]Answer D is equivalent to [tex]\frac{1}{8}[/tex]E.∵ [tex]2^{-2}*2^{5}=2^{-2+5}=2^{3}[/tex]∵ 2³ = 8Answer E is not equivalent to [tex]\frac{1}{8}[/tex]The answers are A , C , D