Problem

Write an expression equivalent to \( \frac{\left(5^{4}\right)^{3} \cdot\left(5^{2}\right)^{2}}{5^{6}} \) using the Laws of Exponents.

Answer

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Answer

\( 5^{10} \)

Steps

Step 1 ：\( \frac{\left(5^{4}\right)^{3} \cdot\left(5^{2}\right)^{2}}{5^{6}} \)

Step 2 ：\( \frac{5^{4 \cdot 3} \cdot 5^{2 \cdot 2}}{5^{6}} \)

Step 3 ：\( \frac{5^{12} \cdot 5^{4}}{5^{6}} \)

Step 4 ：\( 5^{(12 + 4 - 6)} \)

Step 5 ：\( 5^{10} \)

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