Zero and Negative Exponents – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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Negative Exponents may seem confusing but if you know the properties of exponents, solving problems will be much easier to understand, and the strategies to solve the problems will be much easier to remember.

First let’s review the Property of Zero Exponents. The property states that any base raised to the zero power is equal to one – that’s any base. So one million raised to the zero power is equal to one? That’s right.

How will this help us to understand negative exponents? Let’s consider a fraction: The numerator is equal to 7 raised to the zero power, and the denominator is equal to 7 raised to the second power. If we simplify this we get a fraction with 1 as the numerator and 49 as the denominator:

To make this concept easier to understand, use the Quotient of Powers Property. For same bases in the numerator and denominator, simply subtract the exponents, so for this same fraction, we can subtract 2 from 0 to calculate the difference of -2. So 7 raised to the -2 power is equal to Now, this makes sense and since it makes sense, it’s so much easier to remember how to solve problems with negative exponents. Just remember, for a negative exponent, write a 1 in the numerator, and in the denominator, write the base raised to the absolute value of the negative exponent.

To have a laugh and watch some examples of zero and negative exponents, get a bowl or popcorn and watch this video.

Interpret the structure of expressions.


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Exercises in this Practice Problem
Decide what $10^{-5}$ stands for.
Explain why $2^{-4} = \frac1{2^4}$ is true.
Examine the following powers with negative exponents.
Decide the power of the enlarging potion.
Explain how to write $x^{-a}$ as a fraction.
Identify the powers resulting from the calculations shown.