How do you simplify the expression #(16q^0r^-6)/(4q^-3r^-7)# using the properties?

1 Answer
Apr 20, 2017

Answer:

#(16q^0r^-6)/(4q^-3r^-7)=4q^3r#

Explanation:

#(16q^0r^-6)/(4q^-3r^-7)#

#=(16cancelcolor(red)(q^0)cancelcolor(red)(1)r^-6)/(4q^-3r^-7)-># Everything to the power of 0 is 1. Everything multiplied by 1 is itself/the same number.

#=(16cancelcolor(orange)(r^-6)color(blue)(q^3)color(green)(r^7))/(4cancelcolor(blue)(q^-3)cancelcolor(green)(r^-7)color(orange)(r^6))-># Negative exponents will bring the base and its POSITIVE exponent across the fraction bar.

#=(cancelcolor(brown)(16)color(magenta)(4*cancel(4))q^3r^7)/(cancelcolor(magenta)(4)r^6)-># #16=4xx4#. You can now cancel a four in the numerator (above fraction bar) and the denominator (below fraction bar).

#=(4q^3cancelcolor(gold)(r^7)color(gold)(r))/(cancelcolor(gold)(r^6)cancelcolor(gold)(1))-># Cancel like exponents in the numerator and the denominator.

#=4q^3r-># Final answer!