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Evaluate. Write your answer as a whole number or as a simplified fraction.\newline4743=□\frac{4^{7}}{4^{3}}=\square

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Full solution

Q. Evaluate. Write your answer as a whole number or as a simplified fraction.\newline4743=□\frac{4^{7}}{4^{3}}=\square
  1. Identify base and exponents: Identify the base and the exponents in the expression (47)/(43)(4^7)/(4^3).\newlineBase: 44\newlineExponent in the numerator: 77\newlineExponent in the denominator: 33
  2. Apply quotient rule: Apply the quotient rule for exponents which states that when dividing like bases, you subtract the exponents: am/an=a(m−n)a^m / a^n = a^{(m-n)}.\newlineCalculation: 4(7−3)=444^{(7-3)} = 4^4
  3. Calculate value: Calculate the value of 444^4.\newlineCalculation: 44=4×4×4×4=16×16=2564^4 = 4 \times 4 \times 4 \times 4 = 16 \times 16 = 256

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