Powers Examples

What's the value of 3⁴?

Translation: that's a base of 3 with an exponent of 4, which means we're multiplying 4 copies of 3.

3⁴ = 3 × 3 × 3 × 3

Multiply your heart out.

3 × 3 × 3 × 3 =
9 × 3 × 3 =
27 × 3 =
81

What is 3² + 4¹?

First we calculate 3², which is 3 × 3 or 9.

Next we calculate 4¹, which is 4.

Finally we add 9 and 4 to get our final answer.

3² + 4¹ = 9 + 4 = 13

What is (-12.336)⁰?

Don't freak out! This problem looks gnarly, but we picked up a handy rule in the reading. If we raise any number to the power of 0, the answer is just 1.

(-12.336)⁰ = 1

See? Nothin' to it.

What is -10² × (-10)²?

We'll tackle it one step at a time. In the first term, -10², only the 10 is being squared—not the negative.

-10² = -(10 × 10) = -100

In the second term, both the negative and the 10 are being squared. That makes the product positive.

(-10)² = (-10) × (-10) = 100

Now the two terms can combine forces.

-10² × (-10)² =
-100 × 100 

We're multiplying a negative by a positive, so the answer is negative.

-100 × 100 = -10,000

What is 2⁴ + 5⁰?

For starters, we know that anything to the 0th power is just 1. That means 5⁰ = 1, so we can rewrite the problem like so:

2⁴ + 5⁰ =
2⁴ + 1

Ah, much better.

What about 2⁴? Our base is 2 and our exponent is 4, so we're multiplying 2 by itself 4 times.

2⁴ + 1 =
(2 × 2 × 2 × 2) + 1

Finish up by multiplying, then adding.

(2 × 2 × 2 × 2) + 1 =
(4 × 2 × 2) + 1 =
(8 × 2) + 1 =
(16) + 1 =
17