Evaluate 4^8

Problem

4

Solution

1. Rewrite the base as a power of 2 to simplify the calculation.

4=2

2. Apply the power of a power rule, which states (am)n=a(m⋅n)

(2)8=2(2⋅8)

3. Multiply the exponents.

2

4. Calculate the value of 2 by repeated multiplication or by using known powers of 2 (e.g., 2=1024.

2⋅2=1024⋅64

5. Perform the final multiplication.

1024⋅64=65536

Final Answer

4=65536

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