Questions: Evaluate the following expressions.
(-2)^8=
-2^8=
Transcript text: Evaluate the following expressions.
\[
\begin{array}{l}
(-2)^{8}=\square \\
-2^{8}=\square
\end{array}
\]
Check Answer
Solution
Solution Steps
Step 1: Evaluate (−2)8
The expression (−2)8 means that −2 is raised to the 8th power. Since the exponent is even, the result will be positive. We calculate:
(−2)8=(−2)×(−2)×(−2)×(−2)×(−2)×(−2)×(−2)×(−2).
Simplifying step by step:
(−2)2=4,(−2)4=16,(−2)6=64,(−2)8=256.
Thus, (−2)8=256.
Step 2: Evaluate −28
The expression −28 means that 2 is raised to the 8th power first, and then the negative sign is applied. We calculate:
28=2×2×2×2×2×2×2×2=256.
Then, apply the negative sign:
−28=−256.