Simplify. Rewrite the expression in the form 9^(n). (9^(-3))/(9^(12))=◻++^(-x)

Identify base and exponents: Identify the base and the exponents of both the numerator and the denominator. In the numerator, the base is 9 raised to the exponent -3. In the denominator, the base is 9 raised to the exponent 12. Base: 9 Exponent of numerator: -3 Exponent of denominator: 12Apply quotient rule for exponents: Apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponents. Rewrite the expression as a single power of 9. (9^(-3))/(9^(12)) = 9^(-3 - 12)Perform subtraction of exponents: Perform the subtraction of the exponents. 9^(-3 - 12) = 9^(-15)Verify expression form: Verify that the expression is now in the form of 9^(n), where n is the exponent. The expression is now 9^(-15), which is in the form of 9^(n) with n = -15.

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Simplify.

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Rewrite the expression in the form

9^{n}

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\frac{9^{-3}}{9^{12}}=\square

Identify base and exponents: Identify the base and the exponents of both the numerator and the denominator. In the numerator, the base is $9$ raised to the exponent $-3$ . In the denominator, the base is $9$ raised to the exponent $12$ . $\newline$ Base: $9$ $\newline$ Exponent of numerator: $-3$ $\newline$ Exponent of denominator: $12$
Apply quotient rule for exponents: Apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponents. Rewrite the expression as a single power of $9$ . $\newline$ $\left(9^{-3}\right)/\left(9^{12}\right) = 9^{-3 - 12}$
Perform subtraction of exponents: Perform the subtraction of the exponents. $\newline$ $9^{(-3 - 12)} = 9^{-15}$
Verify expression form: Verify that the expression is now in the form of $9^{(n)}$ , where $n$ is the exponent. $\newline$ The expression is now $9^{(-15)}$ , which is in the form of $9^{(n)}$ with $n = -15$ .