Question

Which of the following would be equivalent to 9 to the 2nd power ⋅ 9 to the 6th power?

A) 9 to the 8th power over 9 to the 7th power

B) 9 to the 2nd power ⋅ 9 to the 7th power

C) 9 to the 10th power over 9 to the 2nd power

D) 9 to the power of 0

Answer 1

`\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^( n)} \qquad \qquad \cfrac{1}{a^( n)}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ 9^2\cdot 9^6\implies 9^(2+6)\implies 9^8 \\\\\\ \cfrac{9^(10)}{9^2}\implies 9^(10)\cdot 9^(-2)\implies 9^(10-2)\implies 9^8`

Answer 2

Answer is C)


`9^2*9^6=9^(2+6)= \boxed{9^8}\\\\A) \ (9^8)/(9^7)=9^(8-7)=9^1=9 \\\\B) \ 9^2*9^7=9^(2+7)=9^9 \\\\C) \ (9^(10))/(9^2)=9^(10-2)= \boxed{9^8}\\\\D) \ 9^0=1`