Introduction to Exponents and Powers

Property An exponent indicates how many times the base is used as a factor. For example, $5^3$ means $5 \cdot 5 \cdot 5$. We read expressions with exponents as powers. We say $5^2$ as "five squared" and $10^3$ as "ten cubed.".

Examples $2^5 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32$ Compare $5^2$ and $2^5$: $5^2 = 25$ while $2^5 = 32$, so $5^2 < 2^5$. To simplify $10^2 + 5^2$, calculate the powers first: $100 + 25 = 125$.

Explanation Think of an exponent as a tiny boss telling the big base number how many times to multiply itself. So, $4^3$ isn't a lazy $4 \cdot 3$, but an exciting team up of three fours multiplying together ($4 \cdot 4 \cdot 4$). It’s a super handy shortcut for writing huge multiplication problems and making numbers grow incredibly fast!