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Simplify the expression rac8-1 imes 532-4

Mathematics

ScanSolve AI Answer

Answer

250

Step-by-step solution

5 steps

  1. Rewrite 8 as a power of 2.

    8=238 = 2^3

    Substitute this into the expression:

    (23)−1×532−4\frac{(2^3)^{-1} \times 5^3}{2^{-4}}

  2. Apply the exponent rule (am)n=am×n(a^m)^n = a^{m \times n}.

    2−3×532−4\frac{2^{-3} \times 5^3}{2^{-4}}

  3. Apply the exponent rule aman=am−n\frac{a^m}{a^n} = a^{m-n} for the terms with base 2.

    2−3−(−4)×532^{-3 - (-4)} \times 5^3 2−3+4×532^{-3 + 4} \times 5^3 21×532^1 \times 5^3

  4. Calculate the values of 212^1 and 535^3.

    21=22^1 = 2 53=5×5×5=1255^3 = 5 \times 5 \times 5 = 125

  5. Multiply the results.

    2×125=2502 \times 125 = 250

    The final answer is 250.

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