Simplify (x/y)^8: Evaluating Powers of Fractional Expressions

When you have a fraction raised to a power, you're multiplying that entire fraction by itself 8 times. This means $\frac{x}{y} \times \frac{x}{y} \times \frac{x}{y}...$ which gives $\frac{x^8}{y^8}$.

The first expression $\frac{x^8}{y}$ means the exponent only applied to x, which is incorrect. The second $\frac{x^8}{y^8}$ shows the exponent applied to both parts, which is the correct answer.

No! Don't confuse this with distribution. The expression $\frac{8x}{8y}$ would mean you multiplied 8 times x and y, which is completely different from raising to the 8th power.

Yes! Whether it's $\left(\frac{x}{y}\right)^2$, $\left(\frac{x}{y}\right)^{10}$, or any other power, always apply the exponent to both numerator and denominator.

The same rule applies! For example: $\left(\frac{xy}{z}\right)^3 = \frac{(xy)^3}{z^3} = \frac{x^3y^3}{z^3}$. Each variable gets raised to the power.