Squares and Cubes

Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 2 of 62.

$A 5 by 5 square made of 25 small squares$

A 5 by 5 square holds 25 small squares, so ${5}^{2}$ is read "five squared". A 2 by 2 by 2 cube holds 8 small cubes, so ${2}^{3}$ is "two cubed".

Sometimes you can swap the base and the exponent and get the same number: ${2}^{4}$ and ${4}^{2}$ are both 16. For positive whole numbers, 2 and 4 are the only pair where this works.

Challenge

Is ${3}^{4}$ bigger than, equal to or smaller than ${4}^{3}$ ? Work both out, then choose the sign.

Try it yourself

{3}^{4} \;\boxed{\phantom{>}}\; {4}^{3}

Pick the sign that makes it true

All lessons in Exponents & Polynomials

2The Product Rule

Multiplying Same Bases With Coefficients Recap: The Product Rule

5Product and Quotient Powers

Every Factor Gets the Power With a Number Inside A Power of a Quotient All Three Rules Together Recap: Products and Quotients

8What a Polynomial Is

Terms with Powers The Degree Like Terms, Only Stronger Recap: Meet the Polynomials

11Dividing by a Monomial

Splitting the Fraction Dividing by a Variable Term Bigger Splits Cancel with Care Recap: Dividing