(53⋅5)6

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

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