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Repeated Multiplication

Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 1 of 64.

Multiplication is repeated addition: 3 * 4 means four threes added together. One floor up, a power is repeated multiplication: 2^4 means four twos multiplied together, 2 * 2 * 2 * 2, which is 16.

The number being multiplied is the base; the small raised number counts the copies and is called the exponent. In 2^4 the base is 2, the exponent is 4, and the whole thing is read "two to the fourth". The exponent counts factors, not multiplications: 2^4 has four factors of 2 in it.

A power is a single number wearing compact clothing. Evaluating it means taking the clothing off: 2^4 = 16, 5^2 = 25, 10^3 = 1000. Everything in this section, every rule and every shortcut, unpacks to counting factors.

Challenge

Easy

Unpack 2^5 into its factors, then multiply it down: type each new line until one number remains.

Try it yourself

2^5

Simplify the expression

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Exponents & Polynomials

1What a Power Is

Repeated MultiplicationSquares and Cubes Powers of Negative Numbers Where the Minus Lives Recap: First Powers

4Power of a Power

A Power Raised Again Why Exponents Multiply Product Rule or Power Rule?The Rule in Letters Recap: Power of a Power

7Scientific Notation

Very Large Numbers Back to Standard Form More Practice, Bigger Numbers Very Small Numbers Multiplying the Notation Recap: Scientific Notation

10Multiplying Polynomials

Monomial Times Polynomial Minding the Signs Binomial Times Binomial With Coefficients The Square of a Binomial A Difference of Squares Recap: Multiplying

2The Product Rule

Multiplying Same Bases With Coefficients More Than Two Factors The Rule in Letters 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