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Evaluate the terms with negative exponents using the rule a^-n = (1)/(aⁿ) or ((a)/(b))^-n = ((b)/(a))ⁿ.

Mathematics

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Answer

1964\frac{19}{64}

Step-by-step solution

4 steps

  1. Evaluate the terms with negative exponents using the rule a−n=1ana^{-n} = \frac{1}{a^n} or (ab)−n=(ba)n\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n.

    (13)−3=33=27\left(\frac{1}{3}\right)^{-3} = 3^3 = 27 (12)−3=23=8\left(\frac{1}{2}\right)^{-3} = 2^3 = 8 (14)−3=43=64\left(\frac{1}{4}\right)^{-3} = 4^3 = 64

  2. Substitute these values back into the original expression.

    [27−8]÷64\left[27 - 8\right] \div 64

  3. Perform the subtraction inside the brackets.

    19÷6419 \div 64

  4. Perform the division.

    1964\frac{19}{64}
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QApply the negative exponent rule ((a)/(b))^-n = ((b)/(a))ⁿ.QApply the exponent rule ((a)/(b))ⁿ = (aⁿ)/(bⁿ) to the second term.QRewrite the first term using the exponent rule a^m-n = (a^m)/(aⁿ).QApply the quotient rule for exponents, which states (a^m)/(aⁿ) = a^m-n.QRewrite the terms in the numerator and denominator using exponent rules a^m+n = a^m * aⁿ.
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