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

Math
(9p44y2)12
Use the power rule (ab)n=anbn to distribute the exponent.
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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.
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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.
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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.
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Apply the power rule and multiply exponents, (am)n=amn.
3p4(12)412(y2)12
Cancel the common factor of 2.
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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.
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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.
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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.
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Apply the power rule and multiply exponents, (am)n=amn.
3p22y2(12)
Cancel the common factor of 2.
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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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