# Simplify ((9p^4)/(4y^2))^(1/2)

(9p44y2)12
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to 9p44y2.
(9p4)12(4y2)12
Apply the product rule to 9p4.
912(p4)12(4y2)12
Apply the product rule to 4y2.
912(p4)12412(y2)12
912(p4)12412(y2)12
Simplify the numerator.
Rewrite 9 as 32.
(32)12(p4)12412(y2)12
Apply the power rule and multiply exponents, (am)n=amn.
32(12)(p4)12412(y2)12
Cancel the common factor of 2.
Cancel the common factor.
32(12)(p4)12412(y2)12
Rewrite the expression.
31(p4)12412(y2)12
31(p4)12412(y2)12
Evaluate the exponent.
3(p4)12412(y2)12
Multiply the exponents in (p4)12.
Apply the power rule and multiply exponents, (am)n=amn.
3p4(12)412(y2)12
Cancel the common factor of 2.
Factor 2 out of 4.
3p2(2)12412(y2)12
Cancel the common factor.
3p2⋅212412(y2)12
Rewrite the expression.
3p2412(y2)12
3p2412(y2)12
3p2412(y2)12
3p2412(y2)12
Simplify the denominator.
Rewrite 4 as 22.
3p2(22)12(y2)12
Apply the power rule and multiply exponents, (am)n=amn.
3p222(12)(y2)12
Cancel the common factor of 2.
Cancel the common factor.
3p222(12)(y2)12
Rewrite the expression.
3p221(y2)12
3p221(y2)12
Evaluate the exponent.
3p22(y2)12
Multiply the exponents in (y2)12.
Apply the power rule and multiply exponents, (am)n=amn.
3p22y2(12)
Cancel the common factor of 2.
Cancel the common factor.
3p22y2(12)
Rewrite the expression.
3p22y1
3p22y1
3p22y1
Simplify.
3p22y
3p22y
Simplify ((9p^4)/(4y^2))^(1/2)

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