Question

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

Answer 1

`9\text{ \textasciicircum-16}`

Step-by-step explanation

let's remember some properties of the exponents

`\begin{gathered} a^m\cdot a^n=a^(m+n) \\ (a^m)^n=a^(mn) \\ (a^m)/(a^n)=a^(m-n) \\ a^(-m)=(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