Quotient rule of exponents practice
Sure! Here's a practice problem on the quotient rule of exponents:
Simplify the expression: (2^4 / 2^2)^3
Solution:
To simplify this expression using the quotient rule of exponents, we need to apply the rule, which states that for any non-zero integer a and any integers m and n, (a^m / a^n) = a^(m - n).
In our given expression, we have (2^4 / 2^2)^3. Applying the quotient rule of exponents, we subtract the exponents in the numerator and denominator: 4 - 2 = 2.
So, the expression simplifies to (2^2)^3 = 2^6.
Therefore, the simplified expression is 2^6, which is equal to 64.
The quotient rule of exponents states that when you divide two exponential terms with the same base, you subtract the exponents.
To practice applying the quotient rule of exponents, let's work through a step-by-step example:
Example: Simplify the expression (2^5) / (2^3)
Step 1: Identify the base. In this example, the base is 2.
Step 2: Apply the quotient rule of exponents. Subtract the exponent of the denominator from the exponent of the numerator. 5 - 3 = 2.
Step 3: Rewrite the expression with the simplified exponent. The simplified expression is 2^2.
Step 4: Calculate the value of the expression. 2^2 = 4.
So, (2^5) / (2^3) simplifies to 4.