\[\begin{align*} \boxed{2^3 = 2 \times 2 \times 2 = 8} \end{align*}\]
Introduction
Exponents are a convenient way to represent repeated multiplication, and understanding how to evaluate them is essential in math. The expression \( 2^3 \) is an example of exponential notation, where \( 2 \) is the base, which is the number being multiplied, and \( 3 \) is the exponent, which tells us how many times to multiply the base by itself. In other words, \( 2^3 \) means “multiply 2 by itself 3 times.”
Step-by-Step Solution
To solve \( 2^3 \), we can expand the expression as follows:
\[\begin{align*} \boxed{2^3 = 2 \times 2 \times 2 = 8} \end{align*}\]
Practice Problems
- Evaluate $5^3$.
Rewriting the exponentiation as multiplication, $5^3 = 5 \cdot 5 \cdot 5 = 125$. - Evaluate $10^{10}$.
Working with repeated multiplication of $10$ is the same as adding zeros at the end of a number. We end up with $10000000000$. - Evaluate $(2^4)^2$.
Rewriting the exponentiation as multiplication, notice that $2^4 = 16$, so it would be the same as if we asked for $(16)^2$. Expanding, we get $16^2 = 16 \cdot 16 = 256$.
