Question

c. \\(4^2 \times 2^{-4}\\)

Explanation:

Step1: Rewrite 4 as a power of 2

Since \(4 = 2^2\), we can rewrite \(4^2\) as \((2^2)^2\). Using the exponent rule \((a^m)^n=a^{m\times n}\), we get \((2^2)^2 = 2^{2\times2}=2^4\). So the expression becomes \(2^4\times2^{-4}\).

Step2: Apply the exponent rule for multiplication

The rule for multiplying exponents with the same base is \(a^m\times a^n=a^{m + n}\). Here, \(a = 2\), \(m = 4\), and \(n=- 4\). So \(2^4\times2^{-4}=2^{4+( - 4)}\).

Step3: Simplify the exponent

Calculate \(4+( - 4)=0\). So we have \(2^0\). By the definition of exponents, any non - zero number to the power of 0 is 1, so \(2^0 = 1\).

Answer:

1