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Simplify the expression. (16y^5/4y^3)^1/2 Enter your answer in the box.<img src="-f-.jpg" alt> This is due in 7 minutes!!!!!!

Simplify the expression. (16y^5/4y^3)^1/2 Enter your answer in the box.<img src="-f-.jpg" alt> This is due in 7 minutes!!!!!!
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Simplify the expression. (16y^5/4y^3)^1/2

Enter your answer in the box.

This is due in 7 minutes!!!!!!

Simplify the expression. (16y^5/4y^3)^1/2 Enter your answer in the box.<img src-example-1
User Lynnaloo
by
7.2k points

1 Answer

3 votes

\bf a^{( n)/( m)} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{( n)/( m)}\\\\ -------------------------------\\\\ \left( \cfrac{16y^5}{4y^3} \right)^{(1)/(2)}\implies \left( \cfrac{4^2y^5}{2^2y^3} \right)^{(1)/(2)}\impliedby \textit{let's distribute the exponent}


\bf \left( \cfrac{4^{2\cdot (1)/(2)}y^{5\cdot (1)/(2)}}{2^{2\cdot (1)/(2)}y^{3\cdot (1)/(3)}} \right)\implies \cfrac{4^1y^{(5)/(2)}}{2^1y^1}\implies \cfrac{4y^{(5)/(2)y^(-1)}}{2}\implies \cfrac{4y^{(5)/(2)-1}}{2}\implies \cfrac{4y^{(3)/(2)}}{2} \\\\\\ \cfrac{2y^{(3)/(2)}}{1}\implies 2\sqrt[2]{y^3}\implies 2\sqrt{y^(2+1)}\implies 2√(y^2y)\implies 2y√(y)
User Minsk
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