Select all the expressions that are equivalent to (9^36)/(9^–4). Multi-select Choices: [[9^–40][9^–9][1/(9^–40)][1/(9^–9)]]

Understand operation with exponents: Understand the operation to perform with the exponents. When dividing powers with the same base, we subtract the exponents according to the rule a^m / a^n = a^(m-n).Calculate result of (9^36)/(9^–4): Calculate the result of (9^36)/(9^–4) by subtracting the exponents. 9^36 / 9^–4 = 9^(36 - (–4)) = 9^(36 + 4) = 9^40Determine equivalence of given choices: Determine if the given choices are equivalent to 9^40. - 9^–40 is not equivalent because it represents 1/(9^40). - 9^–9 is not equivalent because it represents 1/(9^9). - 1/(9^–40) is equivalent because it represents 9^40. - 1/(9^–9) is not equivalent because it represents 9^9.

Home

Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Select all the expressions that are equivalent to

\frac{9^{36}}{9^{-4}}

Understand operation with exponents: Understand the operation to perform with the exponents. $\newline$ When dividing powers with the same base, we subtract the exponents according to the rule $\frac{a^m}{a^n} = a^{(m-n)}$ .
Calculate result of $\frac{9^{36}}{9^{-4}}$ : Calculate the result of $\frac{9^{36}}{9^{-4}}$ by subtracting the exponents. $\newline$ $\frac{9^{36}}{9^{-4}} = 9^{(36 - (-4))} = 9^{(36 + 4)} = 9^{40}$
Determine equivalence of given choices: Determine if the given choices are equivalent to $9^{40}$ . $\newline$ - $9^{-40}$ is not equivalent because it represents $\frac{1}{9^{40}}$ . $\newline$ - $9^{-9}$ is not equivalent because it represents $\frac{1}{9^{9}}$ . $\newline$ - $\frac{1}{9^{-40}}$ is equivalent because it represents $9^{40}$ . $\newline$ - $\frac{1}{9^{-9}}$ is not equivalent because it represents $9^{9}$ .