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

(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.
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.
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.
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.
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.
Apply the power rule and multiply exponents, (am)n=amn.
2a2(12)(b34)12
Cancel the common factor of 2.
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.
Apply the power rule and multiply exponents, (am)n=amn.
2ab34⋅12
Multiply 34⋅12.
Multiply 34 and 12.
2ab34⋅2
Multiply 4 by 2.
2ab38
2ab38
2ab38
Simplify (4a^2b^(-3/4))^(1/2)

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