What is the value of c in the equation below?

Explanation:

We'll use the rule

x^y*x^z = x^(y+z)

This says that when we multiply exponential expressions with the same base, we add the exponents. In this case, the base is 2 so x = 2.

The exponents we're adding are -4 and 2

So,

2^(-4)*2^2 = 2^(-4+2) = 2^(-2)

This matches up with the a^b to show that a = 2 and b = -2

Furthermore, we'll use the rule that x^(-y) = 1/(x^y) to go from 2^(-2) to 1/(2^2) = 1/4 which is the value of c.

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step-by-step explanation: