Answer :
Answer:
The correct options are A ,C and F.
Step-by-step explanation:
The given expression is
[tex]81^x[/tex]
Calculate the simplified form of given options.
A.
[tex](9\cdot 9)^x=81^x[/tex]
B.
[tex]9\cdot 9^{2x}=9\cdot (9^2)^x=9(81)^x[/tex]
C.
[tex]9^x\cdot 9^x=(9\cdot 9)^x=81^x[/tex]
D.
[tex]9^2\cdot 9^x=81(9^x)[/tex]
E.
[tex]9\cdot 9^x=9(9^x)[/tex]
F.
[tex]9^{2x}=(9^2)^x=81^x[/tex]
Therefore correct options are A ,C and F.
The correct options are [tex]{\text{A} = {\left( {9 \cdot 9} \right)^x},C = {9^x} \cdot {9^x}{\text{ and }}F = {9^{2x}}.[/tex]
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 [tex]{81^x}[/tex]
The options are as follows,
(A). [tex]{\left( {9 \cdot 9} \right)^x}[/tex]
(B). [tex]9 \cdot {9^{2x}}[/tex]
(C). [tex]{9^x} \cdot {9^x}[/tex]
(D). [tex]{9^x} \cdot {9^2}[/tex]
(E). [tex]9 \cdot {9^x}[/tex]
(F). [tex]{9^{2x}}[/tex]
Explanation:
The expression [tex]{81^x}[/tex] can also be written as follows,
Solve option (A).
[tex]{\left( {9 \cdot 9} \right)^x} = {81^x}[/tex]
Option (A) is correct.
Solve option (B).
[tex]9 \cdot {9^{2x}} = 9 \cdot {\left( {81} \right)^x}[/tex]
Option (B) is not correct.
Solve option (C).
[tex]\begin{aligned}{9^x} \cdot {9^x} &= {9^{x + x}}\\&= {81^x}\\\end{aligned}[/tex]
Option (C) is correct.
Solve option (D).
[tex]{9^2} \cdot {9^x} = 81\left( {{9^x}} \right)[/tex]
Option (D) is not correct.
Solve option (E).
[tex]9 \cdot {9^x} = 9\left( {{9^x}} \right)[/tex]
Option (E) is not correct.
Solve option (F).
[tex]\begin{aligned}{9^{2x}} &= {\left( {{9^2}} \right)^x}\\&= {81^x}\\\end{aligned}[/tex]
Option (A) is correct.
The correct options are [tex]{\text{A} = {\left( {9 \cdot 9} \right)^x},C = {9^x} \cdot {9^x}{\text{ and }}F = {9^{2x}}.[/tex]
Option B, D and E are not correct.
Learn more:
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Number System
Keywords: expression, equivalent, one below, [tex]81^x[/tex], exponents, addition, powers.