Question

Write the expression in exponential form. \sqrt{10} " alt=" \sqrt{10} " align="absmiddle" class="latex-formula">
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Answer 1

Answer: 10^(1/2)

When we use an exponent of 1/2, it is the same as a square root. The more general rule is

$\sqrt{x} = x^{1/2}$

In this case, we plug in x = 10.

The use of a fractional exponent is handy when you want to deal with things like cube roots on a calculator. This is because

$\sqrt[3]{x} = x^{1/3}$

Many calculators don't have a button labeled $\sqrt[3]{}$ but they have the button $x^y$ to allow fractional exponents.