Raising a Fraction to a Power. Online Calculator.

To raise a fraction to the power n, you need to raise the numerator and denominator of the fraction to the power n. For example, ${\displaystyle {\left(\frac{2}{5}\right)}^3}$${\displaystyle =}$${\displaystyle \frac{2^3}{5^3}}$${\displaystyle =}$${\displaystyle \frac{8}{125}}$

To raise a fraction to the power -n with a negative exponent, the numerator and denominator of the fraction must be reversed and the sign of the power must be replaced with its opposite. Then you need to raise the numerator and denominator of the fraction to a power. For example, ${\displaystyle {\left(\frac{2}{7}\right)}^{-4}={\left(\frac{7}{2}\right)}^4=\frac{7^4}{2^4}=150\frac{1}{16}}$

In order to raise a fraction to a power with a fractional exponent, it is necessary to represent the numerator and denominator of the fraction as a radical number raised to a power equal to the numerator of the power, and write the denominator of the power as the index of the root. For example, ${\displaystyle {\left(\frac{3}{8}\right)}^{\frac{2}{9}}}$ $=$${\displaystyle \frac{\sqrt[9]{3^2}}{\sqrt[9]{8^2}}}$$\approx$$0.804$

In order to raise a fraction to a power with a negative fractional exponent, it is necessary to swap the numerator and denominator of the fraction, while the sign of the power changes to the opposite. Then the numerator and denominator of the fraction are represented as a radical number raised to a power equal to the numerator of the degree, and the denominator of the degree is written as the index of the root. For example, ${\displaystyle {\left(\frac{3}{8}\right)}^{-\frac{2}{9}}}$ $=$${\displaystyle \frac{\sqrt[9]{8^2}}{\sqrt[9]{3^2}}}$$\approx$$1.243$