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How do you simplify the expression $\frac{x^{8}}{x^{4}}$ $x^8/x^4$ using the properties?

1 Answer

MathFact-orials.blogspot.com

Jun 10, 2017

$\frac{x^{8}}{x^{4}} = x^{8 - 4} = x^{4}$ $x^8/x^4=x^(8-4)=x^4$ . See below for more ways to get to this answer.

Explanation:

We can do this a few ways:

Use $\frac{x^{a}}{x^{b}} = x^{a - b}$ $x^a/x^b=x^(a-b)$

We can take $\frac{x^{8}}{x^{4}} = x^{8 - 4} = x^{4}$ $x^8/x^4=x^(8-4)=x^4$

Use ${(x^{a})}^{b} = x^{a b}$ $(x^a)^b=x^(ab)$

We can rewrite the numerator:

$\frac{x^{8}}{x^{4}} = \frac{x^{4 \times 2}}{x^{4}} = \frac{{(x^{4})}^{2}}{x^{4}} = \frac{x^{4} x^{4}}{x^{4}} = x^{4}$ $x^8/x^4=(x^(4xx2))/x^4=(x^4)^2/x^4=(x^4x^4)/x^4=x^4$

Use $x^{a} \times x^{b} = x^{a + b}$ $x^axxx^b=x^(a+b)$

We can rewrite the numerator in a different way:

$\frac{x^{8}}{x^{4}} = \frac{x^{4 + 4}}{x^{4}} = \frac{x^{4} x^{4}}{x^{4}} = x^{4}$ $x^8/x^4=(x^(4+4))/x^4=(x^4x^4)/x^4=x^4$

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