Question

Which expression is equivalent to the one below? check all that apply. 81x

Answer 1

The correct options are ${\text{A} = {\left( {9 \cdot 9} \right)^x},C = {9^x} \cdot {9^x}{\text{ and }}F = {9^{2x}}.$

Further explanation:

The associative property is defined as a grouping of multiplication, addition, subtraction and division.

Always use the PEDMAS rule to solve the grouping of multiplication, addition, subtraction and division.

Here, P is parenthesis, E is exponents, M is multiplication, D is division, A is addition and S is subtraction.

Given:

The expression is ${81^x}$

The options are as follows,

(A). ${\left( {9 \cdot 9} \right)^x}$

(B). $9 \cdot {9^{2x}}$

(C). ${9^x} \cdot {9^x}$

(D). ${9^x} \cdot {9^2}$

(E). $9 \cdot {9^x}$

(F). ${9^{2x}}$

Explanation:

The expression ${81^x}$ can also be written as follows,

Solve option (A).

${\left( {9 \cdot 9} \right)^x} = {81^x}$

Option (A) is correct.

Solve option (B).

$9 \cdot {9^{2x}} = 9 \cdot {\left( {81} \right)^x}$

Option (B) is not correct.

Solve option (C).

$\begin{aligned}{9^x} \cdot {9^x} &= {9^{x + x}}\\&= {81^x}\\\end{aligned}$

Option (C) is correct.

Solve option (D).

${9^2} \cdot {9^x} = 81\left( {{9^x}} \right)$

Option (D) is not correct.

Solve option (E).

$9 \cdot {9^x} = 9\left( {{9^x}} \right)$

Option (E) is not correct.

Solve option (F).

$\begin{aligned}{9^{2x}} &= {\left( {{9^2}} \right)^x}\\&= {81^x}\\\end{aligned}$

Option (A) is correct.

The correct options are ${\text{A} = {\left( {9 \cdot 9} \right)^x},C = {9^x} \cdot {9^x}{\text{ and }}F = {9^{2x}}.$

Option B, D and E are not correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Number System

Keywords: expression, equivalent, one below, $81^x$, exponents, addition, powers.

Answer 2

Answer:

The correct options are A ,C and F.

Step-by-step explanation:

The given expression is

$81^x$

Calculate the simplified form of given options.

A.

$(9\cdot 9)^x=81^x$

B.

$9\cdot 9^{2x}=9\cdot (9^2)^x=9(81)^x$

C.

$9^x\cdot 9^x=(9\cdot 9)^x=81^x$

D.

$9^2\cdot 9^x=81(9^x)$

E.

$9\cdot 9^x=9(9^x)$

F.

$9^{2x}=(9^2)^x=81^x$

Therefore  correct options are A ,C and F.