options:
Because the numerator has an exponent of 8 and the denominator has an exponent of 4, when you divide you are left with x^2
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
Because when you are dividing with exponents, you should add the exponents so that you are left with x^12
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
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To simplify \(\frac{x^8}{x^4}\), you can use the rule of exponents that states when you divide like bases, you subtract the exponents:
\[ \frac{x^a}{x^b} = x^{a-b} \]
In this case, \(a = 8\) and \(b = 4\):
\[ \frac{x^8}{x^4} = x^{8-4} = x^4 \]
Therefore, the correct option is:
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 \(x^4\).
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