(0.92)³.(0.08)⁴⁷

Mathematics

ScanSolve AI Answer

Answer

2.147×10−472.147 \times 10^{-47}

Step-by-step solution

4 steps

  1. Calculate (0.92)3(0.92)^3.

    (0.92)3=0.92×0.92×0.92=0.8464×0.92=0.778688(0.92)^3 = 0.92 \times 0.92 \times 0.92 = 0.8464 \times 0.92 = 0.778688

  2. Calculate (0.08)47(0.08)^{47}.

    This is a very small number.
    (0.08)47≈1.407×10−51(0.08)^{47} \approx 1.407 \times 10^{-51} (using a calculator for precision)

  3. Multiply the results from Step 1 and Step 2.

    0.778688×(1.407×10−51)≈1.0956×10−510.778688 \times (1.407 \times 10^{-51}) \approx 1.0956 \times 10^{-51}

  4. Multiply by 19600.

    19600×(1.0956×10−51)=1.96×104×1.0956×10−5119600 \times (1.0956 \times 10^{-51}) = 1.96 \times 10^4 \times 1.0956 \times 10^{-51}
    =(1.96×1.0956)×104−51= (1.96 \times 1.0956) \times 10^{4-51}
    =2.147376×10−47= 2.147376 \times 10^{-47}

    19600×(0.92)3×(0.08)47≈2.147×10−4719600 \times (0.92)^3 \times (0.08)^{47} \approx 2.147 \times 10^{-47}

    The final answer is 2.147×10−472.147 \times 10^{-47}.

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