Simplify (4a^2b^(-3/4))^(1/2)

Math
(4a2b-34)12
Move the negative in front of the fraction.
(4a2b-34)12
Rewrite the expression using the negative exponent rule b-n=1bn.
(4a21b34)12
Multiply 4a21b34.
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Combine 4 and 1b34.
(a24b34)12
Combine a2 and 4b34.
(a2⋅4b34)12
(a2⋅4b34)12
Move 4 to the left of a2.
(4⋅a2b34)12
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to 4a2b34.
(4a2)12(b34)12
Apply the product rule to 4a2.
412(a2)12(b34)12
412(a2)12(b34)12
Simplify the numerator.
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Rewrite 4 as 22.
(22)12(a2)12(b34)12
Apply the power rule and multiply exponents, (am)n=amn.
22(12)(a2)12(b34)12
Cancel the common factor of 2.
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Cancel the common factor.
22(12)(a2)12(b34)12
Rewrite the expression.
21(a2)12(b34)12
21(a2)12(b34)12
Evaluate the exponent.
2(a2)12(b34)12
Multiply the exponents in (a2)12.
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Apply the power rule and multiply exponents, (am)n=amn.
2a2(12)(b34)12
Cancel the common factor of 2.
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Cancel the common factor.
2a2(12)(b34)12
Rewrite the expression.
2a1(b34)12
2a1(b34)12
2a1(b34)12
Simplify.
2a(b34)12
2a(b34)12
Multiply the exponents in (b34)12.
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Apply the power rule and multiply exponents, (am)n=amn.
2ab34⋅12
Multiply 34⋅12.
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Multiply 34 and 12.
2ab34⋅2
Multiply 4 by 2.
2ab38
2ab38
2ab38
Simplify (4a^2b^(-3/4))^(1/2)

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