40x55x-7

Combine 40×5 and 5x-7 into a single radical.

40x55x-7

Factor 5 out of 40×5.

5(8×5)5x-7

Factor 5 out of 5x-7.

5(8×5)5(x-7)

Cancel the common factor.

5(8×5)5x-7

Rewrite the expression.

8x5x-7

8x5x-7

Move x-7 to the numerator using the negative exponent rule 1b-n=bn.

8x5x7

Multiply x5 by x7 by adding the exponents.

Move x7.

8(x7x5)

Use the power rule aman=am+n to combine exponents.

8×7+5

Add 7 and 5.

8×12

8×12

8×12

Factor 4 out of 8.

4(2)x12

Rewrite 4 as 22.

22⋅2×12

Rewrite x12 as (x6)2.

22⋅2(x6)2

Move 2.

22(x6)2⋅2

Rewrite 22(x6)2 as (2×6)2.

(2×6)2⋅2

(2×6)2⋅2

Pull terms out from under the radical.

2×62

Divide ( square root of 40x^5)/( square root of 5x^-7)