Respuesta :

Answer: The answer is D

because x^2^4 power is x^8 and x^2*x^2*x^2*x^2 which is 2+2+2+2 which is x^8

Step-by-step explanation:

it is not C because it would be 4(c^2) which is 4x^2

it is not A because (x^2)(x^4) is 2+4 which is 6 so that means it would be x^6

The exponent equation correctly shows that [tex](x^{2} )^{4}=x^{8}[/tex] is

[tex](x^{2} )^{4}=x^{2}[/tex] × [tex]x^{2}[/tex] × [tex]x^{2}[/tex] × [tex]x^{2}[/tex] = [tex]x[/tex] × [tex]x[/tex] ×[tex]x[/tex] × [tex]x[/tex] × [tex]x[/tex] × [tex]x[/tex] × [tex]x[/tex] × [tex]x[/tex] = [tex]x^{8}[/tex]

Option (D) is correct

What is an exponent law?

Exponents are also called powers or indices. The exponent rules explain how to solve various equations that as you might expect have exponents in them. They are several different kinds of exponent equations.

Given exponent equation

[tex](x^{2} )^{4}=x^{8}[/tex]

[tex](x^{2} )^{4}=x^{2}[/tex] × [tex]x^{2}[/tex] × [tex]x^{2}[/tex] × [tex]x^{2}[/tex]

If the bases are same, then the powers should be added from an exponent law. It is called as product of powers rule.

[tex](a^{m} )^{n} = a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex]

By adding the power, we get

2+2+2+2 = 8

∴   [tex](x^{2} )^{4} =x^{2+2+2+2} = x^{8}[/tex]

Hence, Option (D) is correct

The exponent equation correctly shows that [tex](x^{2} )^{4}=x^{8}[/tex] is

[tex](x^{2} )^{4}=x^{2}[/tex] × [tex]x^{2}[/tex] × [tex]x^{2}[/tex] × [tex]x^{2}[/tex] = [tex]x[/tex] × [tex]x[/tex] ×[tex]x[/tex] × [tex]x[/tex] × [tex]x[/tex] × [tex]x[/tex] × [tex]x[/tex] × [tex]x[/tex] = [tex]x^{8}[/tex]

Learn more about equation here

https://brainly.com/question/11388790

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