Simplify square root of (abc^-2)/(8b^2c)

Math
abc-28b2c
Reduce the expression abc-28b2c by cancelling the common factors.
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Factor b out of abc-2.
b(ac-2)8b2c
Factor b out of 8b2c.
b(ac-2)b(8bc)
Cancel the common factor.
b(ac-2)b(8bc)
Rewrite the expression.
ac-28bc
ac-28bc
Reduce the expression ac-28bc by cancelling the common factors.
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Factor c out of ac-2.
c(ac-3)8bc
Factor c out of 8bc.
c(ac-3)c(8b)
Cancel the common factor.
c(ac-3)c(8b)
Rewrite the expression.
ac-38b
ac-38b
Move c-3 to the denominator using the negative exponent rule b-n=1bn.
a8bc3
Rewrite a8bc3 as (12c)2a2bc.
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Factor the perfect power 12 out of a.
12a8bc3
Rearrange the fraction 12a(2c)2⋅(2bc).
(12c)2a2bc
(12c)2a2bc
Pull terms out from under the radical.
12ca2bc
Rewrite a2bc as a2bc.
12c⋅a2bc
Multiply a2bc by 2bc2bc.
12c(a2bc⋅2bc2bc)
Combine and simplify the denominator.
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Multiply a2bc and 2bc2bc.
12c⋅a2bc2bc2bc
Raise 2bc to the power of 1.
12c⋅a2bc2bc12bc
Raise 2bc to the power of 1.
12c⋅a2bc2bc12bc1
Use the power rule aman=am+n to combine exponents.
12c⋅a2bc2bc1+1
Add 1 and 1.
12c⋅a2bc2bc2
Rewrite 2bc2 as 2bc.
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Use axn=axn to rewrite 2bc as (2bc)12.
12c⋅a2bc((2bc)12)2
Apply the power rule and multiply exponents, (am)n=amn.
12c⋅a2bc(2bc)12⋅2
Combine 12 and 2.
12c⋅a2bc(2bc)22
Cancel the common factor of 2.
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Cancel the common factor.
12c⋅a2bc(2bc)22
Divide 1 by 1.
12c⋅a2bc(2bc)1
12c⋅a2bc(2bc)1
Simplify.
12c⋅a2bc2bc
12c⋅a2bc2bc
12c⋅a2bc2bc
Simplify the numerator.
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Combine using the product rule for radicals.
12c⋅a(2bc)2bc
Remove unnecessary parentheses.
12c⋅a⋅2bc2bc
12c⋅a⋅2bc2bc
Multiply 12c⋅a⋅2bc2bc.
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Multiply 12c and a⋅2bc2bc.
a⋅2bc2c(2bc)
Multiply 2 by 2.
a⋅2bc4c(bc)
Raise c to the power of 1.
a⋅2bc4(b(c1c))
Raise c to the power of 1.
a⋅2bc4(b(c1c1))
Use the power rule aman=am+n to combine exponents.
a⋅2bc4(bc1+1)
Add 1 and 1.
a⋅2bc4(bc2)
a⋅2bc4(bc2)
Reorder factors in a⋅2bc4bc2.
2abc4bc2
Simplify square root of (abc^-2)/(8b^2c)

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