What Does 3 Squared Look Like? Visualizing the Geometry Behind 3 Times 3

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Q1: Why is $3^2$ pronounced "three squared" instead of "three to the second power"?
Both phrases are mathematically accurate. However, "three squared" remains the standard term because raising a number to the power of 2 geometrically computes the surface area of a square whose sides equal that number.

Q2: What is the difference between $3^2$ and $2^3$?
$3^2$ means 3 multiplied by itself once ($3 \times 3$), equaling 9. In contrast, $2^3$ means 2 used as a factor three times ($2 \times 2 \times 2$), which equals 8. Exponents are not commutative; switching the base and exponent yields completely different totals.

Q3: Does squaring a fraction make it larger or smaller?
Squaring numbers greater than 1 increases their value ($3^2 = 9$). However, squaring a proper fraction between 0 and 1 produces a smaller number. For instance, $(1/3)^2$ equals $1/9$, because taking a fraction of a fraction diminishes the original size.