Simplify the Power Expression: 2²/2⁶ Using Exponent Rules

Insert the corresponding expression:

$\frac{2^2}{2^6}=$

Let's solve the expression $\frac{2^2}{2^6}$ using the rules of exponents. Specifically, we'll use the Power of a Quotient Rule for Exponents which states that $\frac{a^m}{a^n} = a^{m-n}$.

• First, identify the base, which is 2, and the exponents. According to the rule, we subtract the exponent in the denominator from the exponent in the numerator.
• In our case, the exponents are 2 (in the numerator) and 6 (in the denominator).
• Subtract the exponent in the denominator from the exponent in the numerator: $2 - 6 = -4$. This gives us $2^{-4}$.
• According to the rule of negative exponents, $a^{-n} = \frac{1}{a^n}$, so we rewrite $2^{-4}$ as $\frac{1}{2^4}$.

Therefore, the expression $\frac{2^2}{2^6}$ simplifies to $\frac{1}{2^4}$.

The solution to the question is: $\frac{1}{2^4}$