Fractions with exponents on top and bottom

Multiply terms with fractional exponents (provided they have the same base) by adding together the exponents.

Fractional exponents calculator

For example:

\(x^{1/3} × x^{1/3} × x^{1/3} = x^{(1/3 + 1/3 + 1/3)}\)
\(= x^1 = x\)

Since ​x​^1/3 means "the cube root of ​x​," it makes perfect sense that this multiplied by itself twice gives the result ​x​.

You may also run into examples like ​x​^1/3 × ​x​^1/3, but you deal with these in exactly the same way:

\(x^{1/3} × x^{1/3} = x^{( 1/3 + 1/3)}\)
\(= x^{2/3}\)

The fact that the expression at the end is still a fractional exponent doesn't make a difference to the process.

This can be simplified if you note that ​x​^2/3 = (​x​^1/3)² = ∛​_x_​². With an expression like this, it doesn't matter whether you take the root or the power first.

This example illustrates how to calculate these:

\(8^{1/3} + 8^{1/3} = 8^{2/3}\)
\(= (\sqrt[3]{8})^2\)

Since the cube root of 8 is easy to work out, tackle this as follows:

\((\sqrt[3]{8})^2 = 2^2 = 4\)

So this means:

\(8^{1/3} + 8^{1

when power is a fraction

what does it mean when an exponent is a fraction