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

Feb 14, 2018

See a solution process below:

#### Explanation:

Substitute $\textcolor{red}{1}$ for each occurrence of $\textcolor{red}{a}$

Substitute $\textcolor{b l u e}{2}$ for each occurrence of $\textcolor{b l u e}{b}$

${\left(- 2 {\textcolor{red}{a}}^{2} \textcolor{b l u e}{b}\right)}^{3} \sqrt{25 {\textcolor{red}{a}}^{4} {\textcolor{b l u e}{b}}^{6}}$ becomes:

${\left(- 2 \times {\textcolor{red}{1}}^{2} \times \textcolor{b l u e}{2}\right)}^{3} \sqrt{25 \times {\textcolor{red}{1}}^{4} \times {\textcolor{b l u e}{2}}^{6}} \implies$

${\left(- 2 \times 1 \times 2\right)}^{3} \sqrt{25 \times 1 \times 64} \implies$

${\left(- 4\right)}^{3} \sqrt{1600} \implies$

$- 64 \times 40 \implies$

$- 2560$

Not sure where you are getting either $- \frac{5}{8}$ or $- \frac{5}{128}$

Feb 14, 2018

The answer is $- \frac{5}{8}$ 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 $- \frac{5}{8}$

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

$\frac{\sqrt{\left(5 \cdot 5\right) \left(8 \cdot 8\right)}}{\left(\text{-} 8\right) \left(8\right)}$

4) Find the square roots in the numerator

( (5 ) (8)) / (("-"8)  (8))

5) Cancel the $8$s

$- \frac{5}{8}$ $\leftarrow$ answer