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

40x55x-7
Combine 40×5 and 5x-7 into a single radical.
40x55x-7
Reduce the expression 40x55x-7 by cancelling the common factors.
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
Reduce the expression by cancelling the common factors.
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
8×12
8×12
8×12
Rewrite 8×12 as (2×6)2⋅2.
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)