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$9^{-3}/9^{12}$ Rewrite the expression in the form $9^n$

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Evaluate numerical expressions involving exponents

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Q.

9^{-3}/9^{12}

Rewrite the expression in the form

9^n

Understand Exponent Properties: Understand the properties of exponents. When dividing expressions with the same base, we subtract the exponents. This is based on the quotient rule of exponents which states that $a^m / a^n = a^{(m-n)}$ for any nonzero number $a$ and any integers $m$ and $n$ .
Apply Quotient Rule: Apply the quotient rule of exponents to the expression $9^{-3}/9^{12}$ . Using the rule from Step $1$ , we subtract the exponent in the denominator from the exponent in the numerator: $(-3) - 12 = -15$ . So, $9^{-3}/9^{12} = 9^{(-3-12)} = 9^{-15}$ .
Rewrite Expression: Rewrite the expression in the form $9n$ . The expression is already in the form of $9n$ , where $n$ is the exponent $-15$ . So, $9^{-3}/9^{12}$ rewritten in the form $9n$ is $9^{-15}$ .

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