Why is (-2a^2b)^3sqrt(25a^4b^6) equal to -5/8 when a=1 and b=2, instead of -5/128?

2 Answers
Feb 14, 2018

See a solution process below:

Explanation:

Substitute color(red)(1) for each occurrence of color(red)(a)

Substitute color(blue)(2) for each occurrence of color(blue)(b)

(-2color(red)(a)^2color(blue)(b))^3sqrt(25color(red)(a)^4color(blue)(b)^6) becomes:

(-2 xx color(red)(1)^2 xx color(blue)(2))^3sqrt(25 xx color(red)(1)^4 xx color(blue)(2)^6) =>

(-2 xx 1 xx 2)^3sqrt(25 xx 1 xx 64) =>

(-4)^3sqrt(1600) =>

-64 xx 40 =>

-2560

Not sure where you are getting either -5/8 or -5/128

Feb 14, 2018

The answer is -(5)/(8) if the question is

sqrt(25 a^4 b^6)  -:  ("-"2 a^2 b)^3

Explanation:

I think that the question isn't printed correctly.

If the question is

sqrt(25 a^4 b^6)  -:  (−2 a^2  b)^3

then the answer is -(5)/(8)

1) Clear the parentheses in the denominator by raising all the factors inside to the power of 3

sqrt(25 a^4 b^6)  -:   ("-"2^3  a^6  b^3)

2) Sub in 1 for a and 2 for b

sqrt((25)   (1^4)  (2^6))  -:  {("-"2^3)  (1^6)  (2^3)}

3) Simplify by expanding the factors

sqrt((5*5)(8*8))/ {("-"8)(8)}

4) Find the square roots in the numerator

( (5 ) (8)) / (("-"8)  (8))

5) Cancel the 8s

-(5)/(8) larr answer