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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.\newline2925= \frac{2^{9}}{2^{5}}=

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Full solution

Q. Evaluate. Write your answer as a whole number or as a simplified fraction.\newline2925= \frac{2^{9}}{2^{5}}=
  1. Identify Base and Exponents: Identify the base and the exponents in the expression.\newlineIn the expression (29)/(25)(2^9)/(2^5), 22 is the base, 99 is the exponent in the numerator, and 55 is the exponent in the denominator.\newlineBase: 22\newlineExponent in numerator: 99\newlineExponent in denominator: 55
  2. Apply Quotient Rule: Apply the quotient rule for exponents.\newlineThe quotient rule states that when dividing like bases with exponents, you subtract the exponent in the denominator from the exponent in the numerator.\newline(29)/(25)=2(9−5)(2^9)/(2^5) = 2^{(9-5)}
  3. Perform Subtraction of Exponents: Perform the subtraction of the exponents. 29−5=242^{9-5} = 2^4
  4. Calculate Value: Calculate the value of 242^4. 24=2×2×2×2=162^4 = 2 \times 2 \times 2 \times 2 = 16

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