Question

How do you multiply `\frac { 2z ^ { 7} } { 9z } \cdot \frac { 2} { z }`?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule of exponents to rewrite the exponents on the `z` terms in the denominators:

`a = a^color(red)(1)`

`(2z^7)/(9z) * 2/z = (2z^7)/(9z^color(red)(1)) * 2/z^color(red)(1)`

Now, multiply the numerators and denominators separately and use this rule of exponents to multiply the `z` terms in the denominator:

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`(2z^7 * 2)/(9z^color(red)(1) * z^color(blue)(1)) = (4z^7)/(9z^(color(red)(1)+color(blue)(1))) = (4z^7)/(9z^2)`

Now, use this rule of exponents to complete the multiplication of the `z` terms:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`(4z^color(red)(7))/(9z^color(blue)(2)) = (4z^(color(red)(7)-color(blue)(2)))/9 = (4z^5)/9`