29.5 to the power 2/3?

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Connie Share
Nov 19, 2017

Answer:

#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

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