# How do you simplify the expression (2m^3n^-1)(8m^4n^-2) using the properties?

Jul 17, 2017

$\frac{16 {m}^{7}}{n} ^ 3$

#### Explanation:

The operation here is multiplication.
The multiplication property which applies to indices is:

If the bases are the same, add the indices.

$2 {m}^{3} {n}^{-} 1 \times 8 {m}^{4} {n}^{-} 2$

$= 2 \times 8 \times {m}^{3} \times {m}^{4} \times {n}^{-} 1 \times {n}^{-} 2$

$= 16 {m}^{7} {n}^{-} 3 \text{ } \leftarrow \left({x}^{-} m = \frac{1}{x} ^ m\right)$

$= \frac{16 {m}^{7}}{n} ^ 3$