Question #24dfc

1 Answer
Nov 19, 2017

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