Positive & Negative Fractional Exponents Game

Positive & Negative Fractional Exponents Game
The Zero Exponent Rule states that any non-zero number raised to the power of zero is always equal to 1. A fractional exponent means you need to find a root of the base number.The denominator of the fraction tells you which root to take (like a square root or cube root). The numerator of the fraction tells you which power to raise the number to. Scroll down the page for a more detailed explanation.
 
This game is a mental math drill designed to help you master fractional exponents (roots and powers) and negative exponents (reciprocals). Scroll down the page for a detailed explanation.

 

 

How to Play the Positive & Negative Fractional Exponents Game
The game presents you with an expression like 27^2/3 or 16^-3/2 and asks you to solve it in your head.
1. The Setup
Timed Mode: If you check the box on the start screen, you have 60 seconds to get as many correct as possible.
Audio: Use the speaker icon to toggle the sound effects.

2. How to Solve the Problems
The exponent tells you two or three specific steps to take. Here is how to break it down:
Step 1: The Denominator (The Root)
The bottom number of the fraction tells you which root to take.
x^1/2 is the square root (\(\sqrt{x}\)).
x^1/3 is the cube root (\(\sqrt[3]{x}\)).

Step 2: The Numerator (The Power)
The top number of the fraction tells you what power to raise the result to.
Example: For 8^2/3, first take the cube root of 8 (which is 2), then square it (2² = 4).

Step 3: The Negative Sign (The Flip)
If there is a minus sign in the exponent, it means you take the reciprocal (flip it into a fraction).
x^-a = \(\frac{1}{x^a}\)
Example: 9^-1/2 → Square root of 9 is 3. Because it’s negative, the answer is 1/3.

Controls & Input
Typing Answers: You can type whole numbers (e.g., 4) or fractions (e.g., 1/8).
Checking: Press the Check button or hit Enter on your keyboard to submit.

The Fractional Exponent Rule
Fractional Exponents
This rule connects exponents and roots. A fractional exponent means you need to find a root of the base number.
The denominator of the fraction tells you which root to take (like a square root or cube root). The numerator of the fraction tells you which power to raise the number to.
The general formula is:
\(x^{a/b} = \sqrt[b]{x^a}\)
if the fraction is negative then get the reciprocal.
\(x^{-a/b} = \frac{1}{\sqrt[b]{x^a}}\)

This video gives a clear, step-by-step approach to use the fractional exponents rule.

• Show Video

 

Free Exponent Games Online
Multiply Exponents	Divide Exponents	Power of a Power
Power of a Product	Negative Exponents	Fractional Exponents

 

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