Simplifying 4^4/4^6
In this article, we will simplify the expression 4^4/4^6.
Understanding Exponents
Before we dive into simplifying the expression, let's quickly review what exponents are. An exponent is a small number that is raised to a power, indicating how many times a base number should be multiplied by itself. For example, in the expression 4^2, the 2 is the exponent and the 4 is the base. To evaluate this expression, we would multiply 4 by itself 2 times, resulting in 16.
Simplifying the Expression
Now, let's simplify the expression 4^4/4^6.
Step 1: Write the Expression with Exponents
First, we can write the expression with exponents as:
4^4 / 4^6
Step 2: Use the Quotient Rule of Exponents
Next, we can use the quotient rule of exponents, which states that when we divide two numbers with the same base, we can subtract the exponents. This means we can rewrite the expression as:
4^(4-6)
Step 3: Simplify the Exponent
Now, we can simplify the exponent by subtracting 6 from 4, resulting in:
4^(-2)
Step 4: Evaluate the Expression
Finally, we can evaluate the expression by raising 4 to the power of -2, which is equal to:
1/16
Final Answer
Therefore, the simplified expression for 4^4/4^6 is:
1/16
I hope this helps! Let me know if you have any questions.
