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tatiyna
3 years ago
15

Can someone PLEASE explain how to simplify square roots with variables and eexponents in them?? I'd also be thankful if you expl

ained step-by-step how to
solve (16x^4)^3/2 and how to simplify 3y^4/3 times 3yx^1/2? I have to do a retake on my math test and I REALLY need help!
Mathematics
1 answer:
Verizon [17]3 years ago
4 0
X^a/b is  \sqrt[b]{x^a} . The way I memorise that is x^1/3 is the cubic root of x. Do you get it? In that case, x is raised to a power of 1 and the cubic root is practically has a power of 3.
In your example, 

\sqrt[ \frac{3}{2} ]{16 x^4} is practically square rooting each term then cubing them individually. Remember when square-rooting any index you halve it. I'll elaborate:

\sqrt{x^4} = x^{2}
\sqrt{16} = 4
Then cube each,
4^3 = 64 
and ( x^{2} )^3 = x^{6}

As for the 2nd part: you must use the rules of indices.
x^{a}  *  x^{b} =  x^{a+b}
So breaking the question up:

3 * 3 = 9
x^{ \frac{1}{2} } stays as is since the 2nd term does not contain x
now: 
y^{ \frac{4}{3} }  * y^{1} =  y^{ \frac{4}{3} + 1 }  =  y^{ \frac{4}{3} +  \frac{3}{3} }  =   y^{ \frac{7}{3} }
This makes your final answer look like this:
9 x^{ \frac{1}{2} }  y^{ \frac{7}{3} }

I hope that helped and good luck in your test!
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