Question

f. $2^7 + 2^9$

Explanation:

Step1: Factor out the common term

Notice that both terms have a common factor of \(2^7\). So we can factor that out:
\(2^7 + 2^9 = 2^7\times(1 + 2^{9 - 7})\)

Step2: Simplify the exponent

Simplify the exponent in the parentheses: \(9 - 7 = 2\), so we have \(2^7\times(1 + 2^2)\)

Step3: Calculate the value inside the parentheses

Calculate \(1 + 2^2 = 1 + 4 = 5\), so now we have \(2^7\times5\)

Step4: Calculate \(2^7\)

We know that \(2^7 = 128\), so then we calculate \(128\times5\)

Step5: Multiply to get the final result

\(128\times5 = 640\)

Alternatively, we can also calculate the original terms directly:

Step1: Calculate \(2^7\)

\(2^7 = 128\)

Step2: Calculate \(2^9\)

\(2^9 = 512\)

Step3: Add the two results

\(128 + 512 = 640\)

Answer:

\(640\)