Respuesta :

Answer: 9^-16

Step-by-step explanation:

If an exponents have the same base and are  being multiplied together, all you do is just add the exponents and make the base stay the same

9[tex]9^{-53} * 9^{37} = 9^{-16}[/tex]

Negative exponents can be rewritten as positive exponents if you put them in the denominator.

[tex]x^{-a}=\frac{1}{x^a}[/tex]

Using this rule, we can rewrite the equation.

[tex]9^{-53}*9^{37}=\frac{1}{9^{53}}*9^{37}[/tex]

[tex]\frac{9^{37}}{9^{53}}[/tex]

Then, we can use exponent division rules.

[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

[tex]\frac{9^{37}}{9^{53}}=9^{37-53}[/tex]

[tex]9^{-16}[/tex] or [tex]\frac{1}{9^{16}}[/tex]

Hope this helps.

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