# How do you simplify  (16a^2b^4)/(-4b^3) times( -4a^5b)/(-8a^3b^2)?

Jul 3, 2016

$- 2 {a}^{4}$

#### Explanation:

Approach multiplication in algebra questions step by step.
Signs, numbers, indices

SIGNS: In this example, the final sign will be negative, because there is an odd number (3) of negative signs.

NUMBERS: cancel where possible.

INDICES: combine the indices of like bases in the numerator and denominator

$\frac{{\cancel{16}}^{2} {a}^{2} {b}^{4}}{- \cancel{4} {b}^{3}} \times \frac{- \cancel{4} {a}^{5} b}{- \cancel{8} {a}^{3} {b}^{2}} \text{ " = " } \frac{- 2 {a}^{2} {b}^{4}}{{b}^{3}} \times \frac{{a}^{5} b}{{a}^{3} {b}^{2}}$

$= \frac{- 2 {a}^{7} {b}^{5}}{{a}^{3} {b}^{5}}$

Subtract indices of like bases

$= - 2 {a}^{4}$