KelpKelp
contestada

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

Respuesta :

[tex]\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[/tex]
Banabanana
Answer is C)

[tex]9^2*9^6=9^{2+6}= \boxed{9^8}\\\\A) \ \frac{9^8}{9^7}=9^{8-7}=9^1=9 \\\\B) \ 9^2*9^7=9^{2+7}=9^9 \\\\C) \ \frac{9^{10}}{9^2}=9^{10-2}= \boxed{9^8}\\\\D) \ 9^0=1[/tex]

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