Simplify the Expression: 2^a ÷ 2^2 Using Exponent Rules

Question

Insert the corresponding expression:

2a22= \frac{2^a}{2^2}=

Video Solution

Step-by-Step Solution

To solve the expression 2a22 \frac{2^a}{2^2} , we will apply the Power of a Quotient Rule for Exponents, which states that when you divide two powers with the same base, you subtract the exponents.

Here are the steps:

  • Identify the base: Both the numerator and the denominator have the same base, which is 2.

  • Apply the quotient rule of exponents: bmbn=bmn \frac{b^m}{b^n} = b^{m-n} . By applying this rule:

    2a22=2a2 \frac{2^a}{2^2} = 2^{a-2} .

Thus, by utilizing the rule, we find that:

2a22=2a2 \frac{2^a}{2^2} = 2^{a-2} .

The solution to the question is: 2a2 2^{a-2}

Answer

2a2 2^{a-2}