4aca2c3

Rewrite 4ac as 22(ac).

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

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.

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.

Cancel the common factor.

2aca2c32(a2c)33

Divide 1 by 1.

2aca2c32(a2c)1

2aca2c32(a2c)1

Simplify.

2aca2c32a2c

2aca2c32a2c

2aca2c32a2c

Rewrite a2c32 as ((a2c)2)13.

2ac(a2c)23a2c

Apply the product rule to a2c.

2ac(a2)2c23a2c

Multiply the exponents in (a2)2.

Apply the power rule and multiply exponents, (am)n=amn.

2aca2⋅2c23a2c

Multiply 2 by 2.

2aca4c23a2c

2aca4c23a2c

Rewrite a4c2 as a3(ac2).

Factor out a3.

2aca3ac23a2c

Add parentheses.

2aca3(ac2)3a2c

2aca3(ac2)3a2c

Pull terms out from under the radical.

2acaac23a2c

Combine exponents.

Rewrite the expression using the least common index of 6.

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.

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.

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.

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).

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

Factor a out of 2aca5c6.

a(2ca5c6)a2c

Cancel the common factors.

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.

2ca5c6ac

Rewrite the expression.

2a5c6a

2a5c6a

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