Four students are trying to determine what number must replace the question (x^2)^?=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? In words explain why.

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shivishivangi1679 shivishivangi1679 · Answer 1 · 2022-06-18T06:12:03+02:00

Joe is correct as the unknown number is 6.

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

Given :

[tex](x^2)^?=x^4\times x^8[/tex]

Let the question mark exponent outside the bracket be y, which needs to be determined

[tex](x^2)^y=x^4\times x^8[/tex]

Simplify the equation by applying exponent rules to either side of the equation:

Apply the rule [tex](a^b)^c = a^{b \times c}[/tex]

[tex](x^2)^y=x^4\times x^8[/tex]

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

Now apply [tex]a^b \times a^c = a^{b+c}[/tex]

[tex](x)^{2y}=x^{4+8}\\\\(x)^{2y}=x^{12}[/tex]

So, the base is the same the exponent will be the same also,

2y = 12

y = 6

Hence, Joe is correct as the unknown number is 6.

Learn more about exponentiation here:

https://brainly.com/question/26938318

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