Q.Simplify: $\dfrac{5^7}{5^4}$.

Dividing two powers of the same base means subtracting the indices.

By the quotient law, $5^7\div5^4=5^{7-4}=5^3=125$.

By the quotient law of indices (same base $5$), subtract the exponents:

Evaluating: $5^3 = 5\times5\times5 = 125$.

Check (independent recomputation): $5^7=78125$ and $5^4=625$; $78125\div625=125$, matching $5^3$ exactly.

Subtracting in the wrong order ($4-7=-3$, giving $5^{-3}=1/125$ instead of $125$) — the exponent of the DENOMINATOR is always subtracted from the exponent of the NUMERATOR, not the other way round.