Exponentiation

When we think of zy^x, z is the coefficient, y is the base and x is the exponent. The exponent is the number of times the base of something is multiplied by itself.

2² = 2 × 2 = 4

2⁴ = 2 × 2 × 2 × 2 = 16

In terms of multiplying and dividing, these are generally done in the same way as we have seen over the course of this book. Here is an example:

2³ × 2⁴ = (2 × 2 × 2) × (2 × 2 × 2 × 2)

= 8 × 16

= 128

= 16 / 8

= 2

Additionally, 2^(3+4) = 2^7 = 2 × 2 × 2 × 2 × 2 × 2 × 2

= (2 × 2 × 2) × (2 × 2 × 2 × 2) = 2³ × 2⁴.

So remember that:

A^(m+n) = A^m × A^n

Sometimes, you may have to raise your exponent to another exponent, but this can easily be done as well:

(4²)³ = (4 × 4)³

16³ = 16 × 16 × 16

= 4096

You might also see negative exponents on the test. To calculate a negative exponent, take the reciprocal of the base and then change the sign of the exponent.

2^(-4) = (1/2)⁴

This can then be further reduced to:

That is about all there is to know about calculating the power of something. You won't find many questions like these on the GMAT, but you'll see a few so be sure you know how to do them.

More Practice from the GMAT® Review 13th Edition: Questions 65, 106, 111, 117, 122