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

Question

Julia Adams · Accepted Answer

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

Eva Abramson · Answer

undefined To simplify the expression $(16q^0r^{-6})/(4q^{-3}r^{-7})$, we can apply the properties of exponents. First, any non-zero number raised to the power of zero is equal to 1, so $q^0 = 1$. Also, negative exponents indicate reciprocal values. Therefore, $r^{-6}$ becomes $1/r^6$ and $r^{-7}$ becomes $1/r^7$. Now, let's simplify the expression:

$$
\frac{16q^0r^{-6}}{4q^{-3}r^{-7}} = \frac{16 \times 1 \times (1/r^6)}{4 \times (1/q^3) \times (1/r^7)} = \frac{16}{4} \times \frac{1}{q^3} \times \frac{r^7}{r^6} = 4 \times \frac{1}{q^3} \times r^{7-6} = 4 \times \frac{1}{q^3} \times r
$$

So, the simplified expression is $4r/q^3$.