Question

What value of n would make this expression equal to 1/81?
9^0 x 9^-4 x 9^n

A) 0
B) 1
C) 2
D) 3
With work or explanation please! :)

Answer 1

\(\bf aa^{-{\color{red} n}} = \cfrac{1}{a^{\color{red} n}}\qquad thus
\\ \quad \\
\cfrac{1}{81}\implies \cfrac{1}{9^{\color{red}{ 2}}}\implies 9^{\color{red}{ -2}}\qquad thus
\\ \quad \\
9^0\cdot 9^4\cdot 9^n\implies 9^{0+4+n}\qquad which\ equals\ 9^{\color{red}{ -2}}\qquad thus
\\ \quad \\

9^{0+4+n}=9^{\color{red}{ -2}}\implies n=?\)

what do you think?

Answer 2

hmmm got a typo but anyhow \(\bf a^{-{\color{red} n}} = \cfrac{1}{a^{\color{red} n}}\qquad thus
\\ \quad \\
\cfrac{1}{81}\implies \cfrac{1}{9^{\color{red}{ 2}}}\implies 9^{\color{red}{ -2}}\qquad thus
\\ \quad \\
9^0\cdot 9^4\cdot 9^n\implies 9^{0+4+n}\qquad which\ equals\ 9^{\color{red}{ -2}}\qquad thus
\\ \quad \\

9^{0+4+n}=9^{\color{red}{ -2}}\implies n=?\)

so.... what do you think?