Powers of Negative Numbers

Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 3 of 62.

${\left(-2\right)}^{2} = 4$

${\left(-2\right)}^{3} = -8$

${\left(-2\right)}^{4} = 16$

Each extra -2 changes the sign. Two negatives make a positive. So an even exponent gives a positive result, and an odd exponent gives a negative result. Even means 2, 4, 6 and so on. Odd means 1, 3, 5 and so on.

So ${\left(-1\right)}^{100}$ is 1, because 100 is even. You do not need 100 multiplications.

Challenge

Work out ${\left(-3\right)}^{3}$ . Write each next line. A line with the wrong value is not accepted.

Try it yourself

\left(-3\right)^{3}

Simplify

All lessons in Exponents & Polynomials

1What a Power Is

Repeated Multiplication Squares and CubesPowers of Negative NumbersWhere 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 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