Question

Simplify x(8)x(4)
(1 point)
Responses

Because when you are dividing with exponents, you should add the exponents so that you are left with x12
Because when you are dividing with exponents, you should add the exponents so that you are left with x to the 12th power

Because the numerator has an exponent of 8 and the denominator has an exponent of 4, when you divide you are left with x2
Because the numerator has an exponent of 8 and the denominator has an exponent of 4, when you divide you are left with x squared

Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the x's cancel you are left with x4
Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the x's cancel you are left with x to the 4th power

Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the x's cancel you are left with x−4

Answer 1

To simplify \( \frac{x^8}{x^4} \), you subtract the exponent in the denominator from the exponent in the numerator, following the rule for division of exponents.

The correct simplification is:

\[
\frac{x^8}{x^4} = x^{8-4} = x^4
\]

So, the response:
"Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the x's cancel you are left with \( x^4 \)" is correct.