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Write the expression as a radical.

User Anzurio
by
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1 Answer

5 votes

Answer:


5√(5)\left(ab\right)^{(3)/(2)}=√(\left(5ab\right)^3)

Explanation:

Let us consider the expression


5√(5)\left(ab\right)^{(3)/(2)}

Writing the expression as a radical

But, let us revise some rules:


√(a)=a^{(1)/(2)}


\left(a^b\right)^c=a^(bc),\:\quad \mathrm{\:assuming\:}a\ge 0


\left(a\cdot \:b\right)^n=a^nb^n

let us solve now


5√(5)\left(ab\right)^{(3)/(2)}


=5^{(3)/(2)}\left(ab\right)^{(3)/(2)}
\:5^{(3)/(2)}=5√(5)


=\left(5ab\right)^{(3)/(2)}


=\left(5ab\right)^{3\cdot (1)/(2)}


=\left(\left(5ab\right)^3\right)^{(1)/(2)}


\mathrm{Apply\:radical\:rule}:\quad √(a)=a^{(1)/(2)}


=√(\left(5ab\right)^3)

Thus,


5√(5)\left(ab\right)^{(3)/(2)}=√(\left(5ab\right)^3)

User Ralphtheninja
by
8.1k points

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