Question
Simplify the exponents. \( \left(2^{2}\right)^{3}=2^{6} \) (Type exponential notation with positive exponents.) Evaluate. \( \left(2^{2}\right)^{3}=\square \) (Type a whole number.)
Ask by Mccoy Burton. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \left(2^{2}\right)^{3} = 2^{6} = 64 \)
Solution
Calculate or simplify the expression \( 2^{2*3} \).
Calculate the value by following steps:
- step0: Calculate:
\(2^{2\times 3}\)
- step1: Multiply the numbers:
\(2^{6}\)
- step2: Evaluate the power:
\(64\)
The simplified form of \( \left(2^{2}\right)^{3} \) is \( 2^{6} \), which is equal to 64.
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Simplify this solution Bonus Knowledge
When you simplify \( \left(2^{2}\right)^{3} \), you use the power of a power property which states that \((a^{m})^{n} = a^{m \cdot n}\). So, applying this property, we multiply the exponents: \(2^{2 \cdot 3} = 2^{6}\). Now, to evaluate \( \left(2^{2}\right)^{3} \), we first calculate \(2^{2}=4\), and then raise it to the third power: \(4^{3} = 4 \times 4 \times 4 = 64\). Thus, \( \left(2^{2}\right)^{3} = 64 \).
