Solve 7⁴ × 8³ × (1/7)⁴: Power and Reciprocal Multiplication

Because $(\frac{1}{7})^4 = \frac{1}{7^4}$, so you get $7^4 \times \frac{1}{7^4} = \frac{7^4}{7^4} = 1$. Any number divided by itself equals 1!

You could, but it's unnecessary work! $7^4 = 2401$ and $8^3 = 512$, but since $7^4$ cancels with $\frac{1}{7^4}$, you just need $8^3 = 512$.

Then nothing would cancel! You'd need to calculate each part separately: $7^4 \times 8^3 \times \frac{1}{6^4}$. Cancellation only works when bases are the same.

Always scan for matching bases with reciprocal relationships! If you see $a^n$ and $(\frac{1}{a})^n$ or $\frac{1}{a^n}$, they will cancel to 1.

Because $(\frac{1}{7})^4 = \frac{1^4}{7^4}$, and any power of 1 equals 1. This helps show that after cancellation, we're left with $8^3 \times 1 = 8^3$.