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.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Number System
Keywords: expression, equivalent, one below, \(81^x\), exponents, addition, powers.