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

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Answer 1 · 2017-04-17T23:50:06

See the entire solution process below:

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#