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$Evaluate. Write your answer as a whole number or as a simplified fraction. (2^(9))/(2^(5))=$

Evaluate. Write your answer as a whole number or as a simplified fraction. $\newline$ $\frac{2^{9}}{2^{5}}=$

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Powers with negative bases

Full solution

Q. Evaluate. Write your answer as a whole number or as a simplified fraction.

\newline

\frac{2^{9}}{2^{5}}=

Identify Base and Exponents: Identify the base and the exponents in the expression. $\newline$ In the expression $(2^9)/(2^5)$ , $2$ is the base, $9$ is the exponent in the numerator, and $5$ is the exponent in the denominator. $\newline$ Base: $2$ $\newline$ Exponent in numerator: $9$ $\newline$ Exponent in denominator: $5$
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ The quotient rule states that when dividing like bases with exponents, you subtract the exponent in the denominator from the exponent in the numerator. $\newline$ $(2^9)/(2^5) = 2^{(9-5)}$
Perform Subtraction of Exponents: Perform the subtraction of the exponents. $2^{9-5} = 2^4$
Calculate Value: Calculate the value of $2^4$ . $2^4 = 2 \times 2 \times 2 \times 2 = 16$

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