Question

Apply the properties of integer exponents to identify all of the expressions equivalent to 1/8.

Answer 1

Answer:

The answers are A , C , D

Step-by-step explanation:

Lets revise the rule of exponent

* $a^{n}*a^{m}=a^{m+n}$

* $\frac{a^{m}}{a^{n}}=a^{m-n}$

* $\frac{1}{a^{-m}}=a^{m}$

* $(\frac{a}{b})^{-m}=(\frac{b}{b})^{m}$

Now lets solve the problem

We need all the expressions equivalent to $\frac{1}{8}$

A.

∵ $2^{-3}=\frac{1}{2^{3}}$

∵ 2³ = 8

∴ $2^{-3}=\frac{1}{8}$

Answer A is equivalent to $\frac{1}{8}$

B.

∵ 2³ = 8

Answer B is not equivalent to $\frac{1}{8}$

C.

∵ 2³ = 8

∴ $\frac{1}{2^{3}}=\frac{1}{8}$

Answer C is equivalent to $\frac{1}{8}$

D.

∵ $2^{2}*2^{-5}=2^{2+-5}=2^{-3}$

∵ $2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}$

Answer D is equivalent to $\frac{1}{8}$

E.

∵ $2^{-2}*2^{5}=2^{-2+5}=2^{3}$

∵ 2³ = 8

Answer E is not equivalent to $\frac{1}{8}$

The answers are A , C , D