Question #d5343

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Answer 1 · 2017-07-04T11:35:53

$x = 4$ $x=4$

I will assume that you want to solve the following equality for $x$ $x$ :

$x^{\frac{5}{2}} = 32$ $x^(5/2)=32$

Using our index laws we can rewrite the left hand side as:

$x^{\frac{5}{2}} = {(x^{\frac{1}{2}})}^{5}$ $x^(5/2)=(x^(1/2))^5$

and the right hand side as:

$32 = 2^{5}$ $32=2^5$

Now we can write both sides of the equality with the same exponent:

${(x^{\frac{1}{2}})}^{5} = {(2)}^{5}$ $(x^(1/2))^5=(2)^5$

The terms in the brackets must be equal to each other, so:

$x^{\frac{1}{2}} = 2$ $x^(1/2)=2$

Square both sides:

${(x^{\frac{1}{2}})}^{2} = 2^{2}$ $(x^(1/2))^2=2^2$

$\Rightarrow x = 4$ $rArrx=4$