Skill: Interpret powers with whole-number exponents

A power tells you to multiply the same factor repeatedly:

• In $b^n$, $b$ is the base.
• $n$ is the exponent, which tells how many times to use the base as a factor.

For example, evaluate $\left(-3\right)^4$.

Step 1: Identify the base and exponent.

The base is $-3$, and the exponent is $4$. This means use $-3$ as a factor four times.

Step 2: Write the expanded product.

$$\left(-3\right)^4=(-3)(-3)(-3)(-3)$$

The parentheses are important because the entire number $-3$ is the base.

Step 3: Multiply the factors.

$$(-3)(-3)=9$$

and

$$(-3)(-3)=9$$

So,

$$9\cdot 9=81$$

Therefore,

$$\boxed{\left(-3\right)^4=81}$$

Remember that a whole-number exponent means repeated multiplication, not multiplication by the exponent. For example, $5^3$ means $5\cdot5\cdot5$, not $5\cdot3$. Also, for any nonzero base, $b^0=1$. Powers of $10$ work the same way: $10^3=10\cdot10\cdot10=1{,}000$.