amberr813
Answered

What is the value of the expression? 9^8/9^-4 times 9^10


\(\frac{9^{8}}{9^{-4}} times 9^{10}\)


A9−48 B. 9−2 C. 92 D. 922

Verified Answer :

\(\dfrac{9^8}{9^{-4}}\cdot9^{10}=\dfrac{9^8\cdot9^{10}}{9^{-4}}\\----------------\\use:\\a^n\cdot a^m=a^{n+m}\ and\ \dfrac{a^n}{a^m}=a^{n-m}\\------------------------\\\dfrac{9^8\cdot9^{10}}{9^{-4}}=\dfrac{9^{8+10}}{9^{-4}}=\dfrac{9^{18}}{9^{-4}}=9^{18-(-4)}=9^{18+4}=\huge\boxed{9^{22}}\leftarrow\boxed{D}\)

\(If\ your\ example\ is:\dfrac{9^8}{9^{-4}\cdot9^{10}}\ then:\\\\\dfrac{9^8}{9^{-4}\cdot9^{10}}=\dfrac{9^8}{9^{-4+10}}=\dfrac{9^8}{9^6}=9^{8-6}=\huge\boxed{9^2}\leftarrow\boxed{C}\)

TSO

\(\frac{9^8}{9^{-4}\times 9^{10}} = \frac{9^8}{9^{-4+10}} = \frac{9^8}{9^6} =9^{8-6} = 9^2\\\\a^b \times a^c = a^{b+c}\\\frac {a^b}{a^c} =a^{b-c}\)

Related Questions