Question

Which expressions are equivalent to the one below? Check all that apply. 9X O A. (3:3) * O B. 3x. 3x c. 32.31 O D. 3.32% O E. 3. 34 F. 32x

Answer 1

Given:

$9^x\text{ is the given expression.}$

Required:

To find the equivalent expressions from the given options.

Explanation:

We have to simplify all the expressions and know which expressions are equal to the given expression.

$\begin{gathered} (3\cdot3)^x=9^x \\ 3^x\cdot3^x=3^{2x}=(3^2)^x=9^x \\ 3^2\cdot3^x=3^{2+x} \\ 3\cdot3^{2x}=3^{1+2x} \\ 3\cdot3^x=3^{1+x} \\ 3^{2x}=(3^2)^x=9^x \end{gathered}$

Expressions equivalent to the given expression are,

$(3\cdot3)^x,\text{ }3^x\cdot3^x,\text{ }3^{2x}$

Final Answer:

$(3\cdot3)^x,(\text{3})^x\cdot3^x,(\text{3})^{2x}$

Options A,B and F are the correct answers.