((10^2 )^4×(5^3 )^4)/((5^2 )^2×(10^2 )^5 )

asked by guest
on Mar 16, 2025 at 7:51 am



You asked:

Evaluate the expression: 10245345221025\frac{{{10}^{2}}^{4} {{5}^{3}}^{4}}{{{5}^{2}}^{2} {{10}^{2}}^{5}}

MathBot Answer:

10245345221025=156254=3906.25\frac{{{10}^{2}}^{4} {{5}^{3}}^{4}}{{{5}^{2}}^{2} {{10}^{2}}^{5}} = \frac{15625}{4} = 3906.25

10245345221025=10045345221025=1000000005345221025=100000000⋅12545221025=100000000⋅2441406255221025=244140625000000005221025=244140625000000002521025=244140625000000006251025=24414062500000000625⋅1005=24414062500000000625⋅10000000000=244140625000000006250000000000=156254\begin{aligned}\frac{{{10}^{2}}^{4} {{5}^{3}}^{4}}{{{5}^{2}}^{2} {{10}^{2}}^{5}}&=\frac{{100}^{4} {{5}^{3}}^{4}}{{{5}^{2}}^{2} {{10}^{2}}^{5}}\\&=\frac{100000000 {{5}^{3}}^{4}}{{{5}^{2}}^{2} {{10}^{2}}^{5}}\\&=\frac{100000000 \cdot {125}^{4}}{{{5}^{2}}^{2} {{10}^{2}}^{5}}\\&=\frac{100000000 \cdot 244140625}{{{5}^{2}}^{2} {{10}^{2}}^{5}}\\&=\frac{24414062500000000}{{{5}^{2}}^{2} {{10}^{2}}^{5}}\\&=\frac{24414062500000000}{{25}^{2} {{10}^{2}}^{5}}\\&=\frac{24414062500000000}{625 {{10}^{2}}^{5}}\\&=\frac{24414062500000000}{625 \cdot {100}^{5}}\\&=\frac{24414062500000000}{625 \cdot 10000000000}\\&=\frac{24414062500000000}{6250000000000}\\&=\frac{15625}{4}\end{aligned}

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