Divide ( square root of 4ac)/( cube root of a^2c)

Math
4aca2c3
Simplify the numerator.
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Rewrite 4ac as 22(ac).
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Rewrite 4 as 22.
22aca2c3
Add parentheses.
22(ac)a2c3
22(ac)a2c3
Pull terms out from under the radical.
2aca2c3
2aca2c3
Multiply 2aca2c3 by a2c32a2c32.
2aca2c3⋅a2c32a2c32
Combine and simplify the denominator.
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Multiply 2aca2c3 and a2c32a2c32.
2aca2c32a2c3a2c32
Raise a2c3 to the power of 1.
2aca2c32a2c31a2c32
Use the power rule aman=am+n to combine exponents.
2aca2c32a2c31+2
Add 1 and 2.
2aca2c32a2c33
Rewrite a2c33 as a2c.
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Use axn=axn to rewrite a2c3 as (a2c)13.
2aca2c32((a2c)13)3
Apply the power rule and multiply exponents, (am)n=amn.
2aca2c32(a2c)13⋅3
Combine 13 and 3.
2aca2c32(a2c)33
Cancel the common factor of 3.
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Cancel the common factor.
2aca2c32(a2c)33
Divide 1 by 1.
2aca2c32(a2c)1
2aca2c32(a2c)1
Simplify.
2aca2c32a2c
2aca2c32a2c
2aca2c32a2c
Simplify the numerator.
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Rewrite a2c32 as ((a2c)2)13.
2ac(a2c)23a2c
Apply the product rule to a2c.
2ac(a2)2c23a2c
Multiply the exponents in (a2)2.
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Apply the power rule and multiply exponents, (am)n=amn.
2aca2⋅2c23a2c
Multiply 2 by 2.
2aca4c23a2c
2aca4c23a2c
Rewrite a4c2 as a3(ac2).
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Factor out a3.
2aca3ac23a2c
Add parentheses.
2aca3(ac2)3a2c
2aca3(ac2)3a2c
Pull terms out from under the radical.
2acaac23a2c
Combine exponents.
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Rewrite the expression using the least common index of 6.
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Use axn=axn to rewrite ac as (ac)12.
2a((ac)12ac23)a2c
Rewrite (ac)12 as (ac)36.
2a((ac)36ac23)a2c
Rewrite (ac)36 as (ac)36.
2a((ac)36ac23)a2c
Use axn=axn to rewrite ac23 as (ac2)13.
2a((ac)36(ac2)13)a2c
Rewrite (ac2)13 as (ac2)26.
2a((ac)36(ac2)26)a2c
Rewrite (ac2)26 as (ac2)26.
2a((ac)36(ac2)26)a2c
2a((ac)36(ac2)26)a2c
Combine using the product rule for radicals.
2a(ac)3(ac2)26a2c
Apply the product rule to ac.
2aa3c3(ac2)26a2c
Apply the product rule to ac2.
2aa3c3a2(c2)26a2c
Multiply a3 by a2 by adding the exponents.
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Move a2.
2aa2a3c3(c2)26a2c
Use the power rule aman=am+n to combine exponents.
2aa2+3c3(c2)26a2c
Add 2 and 3.
2aa5c3(c2)26a2c
2aa5c3(c2)26a2c
Multiply the exponents in (c2)2.
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Apply the power rule and multiply exponents, (am)n=amn.
2aa5c3c2⋅26a2c
Multiply 2 by 2.
2aa5c3c46a2c
2aa5c3c46a2c
Multiply c3 by c4 by adding the exponents.
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Move c4.
2aa5(c4c3)6a2c
Use the power rule aman=am+n to combine exponents.
2aa5c4+36a2c
Add 4 and 3.
2aa5c76a2c
2aa5c76a2c
2aa5c76a2c
Rewrite a5c7 as c6(a5c).
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Factor out c6.
2aa5(c6c)6a2c
Reorder a5 and c6.
2ac6a5c6a2c
Add parentheses.
2ac6(a5c)6a2c
2ac6(a5c)6a2c
Pull terms out from under the radical.
2a(ca5c6)a2c
2a(ca5c6)a2c
Cancel the common factor of a and a2.
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Factor a out of 2aca5c6.
a(2ca5c6)a2c
Cancel the common factors.
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Factor a out of a2c.
a(2ca5c6)a(ac)
Cancel the common factor.
a(2ca5c6)a(ac)
Rewrite the expression.
2ca5c6ac
2ca5c6ac
2ca5c6ac
Cancel the common factor of c.
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Cancel the common factor.
2ca5c6ac
Rewrite the expression.
2a5c6a
2a5c6a
Divide ( square root of 4ac)/( cube root of a^2c)

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