Question

Use a is calculator to evaluate the expression. Round the result to two decimal places when appropriate. $$\left(2^{4} \cdot 2^{4}\right)^{2}$$

Short answer

The solution to the expression \(\left(2^{4} \cdot 2^{4}\right)^{2}\) is 65536.

Step-by-step solution

Understand the Expression

The expression provided is \(\left(2^{4} \cdot 2^{4}\right)^{2}\). This means '2 raised to the power 4, multiplied by 2 raised to the power 4, and all this is then raised to the second power.'.

Apply Exponents Rules

First we simplify the expression inside the parentheses. Two to power of 4 equals 16, so 16 times 16 equals 256. Now we can simplify the expression into \(256^{2}\).

Calculate the Simplified Expression

Next execute the raised to the power of 2. 256 squared equals 65536.