Algebra Know-It-ALL

116 Powers and Roots

15,6251/6= 5

1 1/2= 1

You can indicate that you want to use the negative value by placing minus signs like this:

−(161/4)=− 2

−(811/4)=− 3

−(15,6251/6)=− 5

−(11/2)=− 1

Sometimes you will actually want to let either the positive or the negative value be used. In cases of that

sort, you should throw a plus-or-minus sign (±) into the mix, like this:

±(161/4)=± 2

±(811/4)=± 3

±(15,6251/6)=± 5

±(11/2)=± 1

Here’s another possible confusion-maker. Always pay special attention to where the parentheses are placed

if you see a negative number raised to a power. Also, be careful if there are no parentheses at all. If there’s

any doubt, it’s best to place extra parentheses in an expression so everyone knows exactly what it means.

For example,

(−2)^3 = (−2) × (−2) × (−2)=− 8

and

− 23 =−(2^3 )

=−(2 × 2 × 2)

=− 8

In contrast to this,

(−2)^4 = (−2) × (−2) × (−2) × (−2)= 16

but

− 24 =−(2^4 )

=−(2 × 2 × 2 × 2)

=− 16

Negative reciprocal powers

We still have not explored what happens when we raise a number to a negative reciprocal-of-

integer power. You can probably figure out the meaning of an expression such as 125−1/3, or