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Exponents of a 0 and 1
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What does it mean to have powers of 0 or 1? We can use the rules we’ve been learning to discover what these mean.

Rules of Exponents-Exponents of 0 and 1

Any number to the 1 power is just itself and any number to the 0 power is 1. Remember that the only exception to this rule is 0 raised to the 0 power.

### Practice Problems

Evaluate the following expressions:
1. $$3^{1}=?$$ (
Solution
Solution:
3
Details:
Any number raised to the power of 1 is still itself, so $$3^{1}$$ is just 3.

This is because the exponent means the number of 3’s being multiplied together.
)
2. $${\text{y}}^{1}=?$$ (
Solution
Solution:
y
)
3. $$5^{0}=?$$ (
Solution
Solution:
1
Details:
Any number raised to the power of 0 is 1.

The following explains why:

We can prove this using what we know about division and the quotient rule. First, we know that anything divided by itself equals 1. For example, $$\dfrac{7}{7}=1$$ or $$\dfrac{\text{m}}{\text{m}}= 1$$. Therefore, something like $$\dfrac{5^{1}}{5^{1}}=\dfrac{5}{5}=1$$ since this is 5 divided by itself. Using the quotient rule, we also know that $$\dfrac{5^{1}}{5^{1}}=5^{(1-1)}=5^{0}$$. The rest is a matter of logic. If $$\dfrac{5^{1}}{5^{1}}=1$$ and $$\dfrac{5^{1}}{5^{1}} =5^{0}$$, then $$5^{0} = 1$$ as well.
)
4. $${\text{b}}^{0}=?$$ (
Solution
Solution:
1
)
5. $$6^{(8-8)}=?$$ (
Video Solution
Solution:
1
Details:

(Video Source | Transcript)
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6. $$\dfrac{{\text{x}}^{9}}{{\text{x}}^{9}}=?$$ (
Video Solution
Solution:
1
Details:

(Video Source | Transcript)
)

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