Simplify the Complex Fraction: 1/(X^7/X^6) Step by Step

Dividing by a fraction is the same as multiplying by its reciprocal. So $\frac{1}{\frac{x^7}{x^6}}$ becomes $1 \times \frac{x^6}{x^7}$, which simplifies to $x^{-1}$.

They're exactly the same thing! $x^{-1}$ is just the exponential notation for $\frac{1}{x}$. Negative exponents always mean 'one over' that base raised to the positive exponent.

Think of it as canceling out: $\frac{x^7}{x^6}$ means you have 7 x's on top and 6 x's on bottom. After canceling, you're left with 7 - 6 = 1 x on top, so $x^1 = x$.

It's much harder that way! Always simplify step by step: first handle $\frac{x^7}{x^6} = x$, then solve $\frac{1}{x} = x^{-1}$. Breaking it into steps prevents mistakes.

Because we have 1 divided by x, not just x! When you have $\frac{1}{x}$, that's the definition of $x^{-1}$. The negative exponent shows we're taking the reciprocal.