The equivalent expressions are:
Option B [tex]7^{2x}[/tex]
Option D [tex]7^x \times 7^x[/tex]
Option E [tex](7 \times 7)^x[/tex]
Solution:
Given expression is:
[tex]49^x[/tex]
We have to find the equivalent expressions
Option A
[tex]7 \times 7^x[/tex]
Use the law of exponent
[tex]a^m \times a^n = a^{ m + n}[/tex]
Therefore,
[tex]7 \times 7^x = 7^{ 1 + x}[/tex]
Thus, option A is not equivalent to given expression
Option B
[tex]a^{mn} = (a^m)^n[/tex]
[tex]7^{2x} =( 7^2)^x = 49^x[/tex]
Thus option B is equivalent to given expression
Option C
Use the law of exponent
[tex]a^m \times a^n = a^{ m + n}[/tex]
[tex]7^2 \times 7^x = 7^{ 2 + x} = 49 \times 7^x[/tex]
Thus, option C is not equivalent to given expression
Option D
[tex]7^x \times 7^x = 7^{ x + x } = 7^{2x}[/tex]
[tex]a^{mn} = (a^m)^n[/tex]
Therefore,
[tex]7^{2x} = (7^2)^x = 49^x[/tex]
Thus option D is equivalent to given expression
Option E
[tex](7 \times 7 )^x = 49^x[/tex]
Thus option E is equivalent to given expression
Option F
[tex]7 \times 7^{2x} = 7^{1 + 2x}[/tex]
Thus, option F is not equivalent to given expression
