# Simplify ( cube root of 5* square root of 5)^6

(53⋅5)6
Multiply 535.
Rewrite the expression using the least common index of 6.
Use axn=axn to rewrite 53 as 513.
(5135)6
Rewrite 513 as 526.
(5265)6
Rewrite 526 as 526.
(5265)6
Use axn=axn to rewrite 5 as 512.
(526⋅512)6
Rewrite 512 as 536.
(526⋅536)6
Rewrite 536 as 536.
(526536)6
(526536)6
Combine using the product rule for radicals.
52⋅5366
Multiply 52 by 53 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
52+366
Add 2 and 3.
5566
5566
5566
Raise 5 to the power of 5.
312566
Rewrite 312566 as 3125.
Use axn=axn to rewrite 31256 as 312516.
(312516)6
Apply the power rule and multiply exponents, (am)n=amn.
312516⋅6
Combine 16 and 6.
312566
Cancel the common factor of 6.
Cancel the common factor.
312566
Divide 1 by 1.
31251
31251
Evaluate the exponent.
3125
3125
Simplify ( cube root of 5* square root of 5)^6

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