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

(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

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

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

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

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

Simplify.

3p22y

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

Solving MATH problems