Question

what is the value of c in the equation below?

(2^{-4} \cdot 2^{2} = a^{b} = c)

-4
-2
(\frac{1}{64})
(\frac{1}{4})

Explanation:

Simplify the product of powers

$$ 2^{-4} \cdot 2^{2} = 2^{-4 + 2} = 2^{-2} $$

Evaluate the negative exponent

$$ 2^{-2} = \frac{1}{2^2} = \frac{1}{4} $$

Identify the value of c

$$ c = \frac{1}{4} $$

Answer:

• (A) \(-4\)
• (B) \(-2\)
• (C) \(\frac{1}{64}\)
• (D) \(\frac{1}{4}\) (Correct answer)