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Evaluate. Write your answer as a whole number or as a simplified fraction.\newline106103=□\frac{10^{6}}{10^{3}}=\square

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Full solution

Q. Evaluate. Write your answer as a whole number or as a simplified fraction.\newline106103=□\frac{10^{6}}{10^{3}}=\square
  1. Identify base and exponents: Identify the base and the exponents.\newlineIn the expression (106)/(103)(10^{6})/(10^{3}), 1010 is the base, 66 is the exponent in the numerator, and 33 is the exponent in the denominator.\newlineBase: 1010\newlineExponent in numerator: 66\newlineExponent in denominator: 33
  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(106)/(103)=106−3(10^{6})/(10^{3}) = 10^{6-3}
  3. Perform subtraction of exponents: Perform the subtraction of the exponents. 10(6−3)=10310^{(6-3)} = 10^{3}
  4. Simplify the expression: Simplify the expression.\newline10310^{3} is the same as 1010 multiplied by itself 33 times.\newline103=10×10×10=100010^{3} = 10 \times 10 \times 10 = 1000

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