# How do you multiply (2a)/(7b^3)div(10a^5)/77?

Jul 12, 2016

$\frac{11}{5 {a}^{4} {b}^{3}}$

#### Explanation:

To change division to multiplication , in fractions, we take the 'reciprocal' (turn fraction upside down) of the divisor.

color(red)(|bar(ul(color(white)(a/a)color(black)(a/b ÷c/d=a/bxxd/c)color(white)(a/a)|)))

rArr(2a)/(7b^3)÷(10a^5)/(77)=(2a)/(7b^3)xx(77)/(10a^5)

Now that we are multiplying the 2 fractions we can cancel any common factors on the numerators/denominators.

$\frac{{\cancel{2}}^{1} {\textcolor{red}{\cancel{a}}}^{1}}{{\textcolor{b l u e}{\cancel{7}}}^{1} {b}^{3}} \times \frac{{\textcolor{b l u e}{\cancel{77}}}^{11}}{{\cancel{10}}^{5} {\textcolor{red}{\cancel{{a}^{5}}}}^{4}} = \frac{1 \times 1 \times 11}{1 \times {b}^{3} \times 5 \times {a}^{4}}$

rArr(2a)/(7b^3)÷(10a^5)/(77)=11/(5a^4b^3