How do you simplify $\frac{c^{7} d^{3}}{c^{3} d^{5}}$ $(c^7d^3)/(c^3d^5)$ ?

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Answer 1 · 2016-12-23T13:24:50

$c^{4} d^{- 2}$ $c^4d^-2$ or $\frac{c^{4}}{d^{2}}$ $c^4/d^2$

To simplify this there are two rules of exponents we can use:

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

and

$\frac{x^{a}}{x^{b}} = \frac{1}{x^{b - a}}$ $color(red)(x^a/x^b = 1/x^(b-a))$

So we can simplify this expression in one of two ways:

First simplification:

$\frac{c^{7} d^{3}}{c^{3} d^{5}} \to c^{7 - 3} d^{3 - 5} \to c^{4} d^{- 2}$ $(c^7d^3)/(c^3d^5) -> c^(7-3)d^(3-5) -> c^4d^-2$

Second simplification:

$\frac{c^{7} d^{3}}{c^{3} d^{5}} \to \frac{c^{7 - 3}}{d^{5 - 3}} \to \frac{c^{4}}{d^{2}}$ $(c^7d^3)/(c^3d^5) -> c^(7-3)/d^(5-3) -> c^4/d^2$

How do you simplify c7d3c3d5(c^7d^3)/(c^3d^5)?