Question

Which expressions are equivalent to the one below? Check all that apply. 212 32

Answer 1

Given:

$\frac{21^x}{3^x}$

Aim:

We need to find the equivalent expression for the given expression.

Explanation:

$Use\text{ }\frac{a^n}{b^n}=(\frac{a}{b})^n.\text{ Here a=21, b=3 and n=x.}$

$\frac{21^x}{3^x}=(\frac{21}{3})^x$$Use\text{ 21=7}\times3\text{ in the given expression.}$

$\frac{21^x}{3^x}=\frac{(7\times3)^x}{3^x}$$Use\text{ }(a\times b)^x=a^x\times b^x.\text{ Here a=7, b=3 and n=x.}$

$\frac{21^x}{3^x}=\frac{7^x\times3^x}{3^x}$

Cancel out common terms.

$\frac{21^x}{3^x}=7^x$

Final answer:

$B.\frac{7^x\times3^x}{3^x}$

$C.\text{ }7^x$

$D.\text{ }(\frac{21}{3})^x$