Question
Simplify:$\frac{3^{5} \times 10^{5} \times 25}{5^{7} \times 6^{5}}$
✓
Answer
$\frac{3^{5} \times 10^{5} \times 25}{5^{7} \times 6^{5}}=\frac{3^{5} \times(2 \times 5)^{5} \times 5^{2}}{5^{7} \times(2 \times 3)^{5}}$
= $\frac{3^{5} \times 2^{5} \times 5^{5} \times 5^{2}}{5^{7} \times 2^{5} \times 3^{5}}$
= $\frac{3^{5} \times 2^{5} \times 5^{5+2}}{2^{5} \times 3^{5} \times 5^{7}}=\frac{2^{5} \times 3^{5} \times 5^{7}}{2^{5} \times 3^{5} \times 5^{7}}$
$=2^{5-5} \times 3^{5-5} \times 5^{7-7}$
$=2^0 \times 3^0 \times 5^0$
$=1 \times 1 \times 1=1$
= $\frac{3^{5} \times 2^{5} \times 5^{5} \times 5^{2}}{5^{7} \times 2^{5} \times 3^{5}}$
= $\frac{3^{5} \times 2^{5} \times 5^{5+2}}{2^{5} \times 3^{5} \times 5^{7}}=\frac{2^{5} \times 3^{5} \times 5^{7}}{2^{5} \times 3^{5} \times 5^{7}}$
$=2^{5-5} \times 3^{5-5} \times 5^{7-7}$
$=2^0 \times 3^0 \times 5^0$
$=1 \times 1 \times 1=1$
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