Question

Question #24dfc

Answer 1

`29.5^(2/3)`. Okay.

Explanation:

Fractional exponents are another way of writing a number that is under a radical and raised to a power.

`29.5^(2/3)` is the same as the cube root of 29.5 squared:

`root(3)(29.5)^2`.

With a fractional exponent, the denominator of the fraction is the root, and the numerator is the power.

`x^(1/2)` is the same as `sqrt(x)`; `root(3)x` is the same as `x^(1/3)`.

In some expressions or equations, you can't work with radical signs, so you use fractional exponents instead.

For this one, if you need a value, use your calculator. You can do either operation first:

square `29.5` and then take the cube root of that, or

take the cube root of `29.5` and then square that, or

enter into your calculator: 29.5 ^ (2/3). Either way, you should get a non-repeating, non-terminating decimal:

`9.547317028.......` is what my calculator says.

PS, if your calculator doesn't have a cube root or an nth root button, use the caret `^` followed by the fraction `1/3` in parentheses.

Connie