Question

9- 53 . 9 37. I need help with the answer

Answer 1

$9\text{ \textasciicircum-16}$

Explanation

let's remember some properties of the exponents

$\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^m)^n=a^{mn} \\ \frac{a^m}{a^n}=a^{m-n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}$

so, to solve this we need to use the first property

$a^m\cdot a^n=a^{m+n}$

( when multiplicating two exponent number, let the base(a) and add the exponents ( m+n)

so

Step 1

$\begin{gathered} 9^{-53}\cdot9^{37} \\ let\text{ the same base and add the exponents} \\ 9^{-53}\cdot9^{37}=9^{-53+37} \\ 9^{-53}\cdot9^{37}=9^{-16} \end{gathered}$

therefore, the answer is

$\begin{gathered} 9^{-16} \\ or \\ 9\text{ \textasciicircum-16} \end{gathered}$

I hope this helps you