Multiplying the Notation
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 36 of 64.
Scientific notation multiplies beautifully, because multiplication reorders. (2 * 10^3)(3 * 10^2): gather the front numbers, 2 * 3 = 6, and gather the powers of ten by the product rule, 10^3 * 10^2 = 10^5. The product is 6 * 10^5, which is 600000.
Fronts multiply, exponents add: the same two-track habit as coefficients and powers of x, because it is literally the same mathematics with base ten.
One wrinkle waits here: if the fronts multiply past 10, say 4 * 5 = 20, the result 20 * 10^6 needs one more shift to return to format: 2 * 10^7. Finish by checking the front.
Challenge
EasyMultiply 4 * 10^2 * (2 * 10^3) in your head: fronts together, exponents together. Type the single power form, then standard form.
Try it yourself
Simplify the expression
Test yourselfThis 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 CubesPowers of Negative NumbersWhere the Minus LivesRecap: First Powers4Power of a Power
A Power Raised AgainWhy Exponents MultiplyProduct Rule or Power Rule?The Rule in LettersRecap: Power of a Power7Scientific Notation
Very Large NumbersBack to Standard FormMore Practice, Bigger NumbersVery Small NumbersMultiplying the NotationRecap: Scientific Notation2The Product Rule
Multiplying Same BasesWith CoefficientsMore Than Two FactorsThe Rule in LettersRecap: The Product Rule5Product and Quotient Powers
Every Factor Gets the PowerWith a Number InsideA Power of a QuotientAll Three Rules TogetherRecap: Products and Quotients8What a Polynomial Is
Terms with PowersThe DegreeLike Terms, Only StrongerRecap: Meet the Polynomials11Dividing by a Monomial
Splitting the FractionDividing by a Variable TermBigger SplitsCancel with CareRecap: Dividing3The Quotient Rule
Dividing Same BasesWhy Exponents SubtractWith CoefficientsThe Rule in LettersRecap: The Quotient Rule6Zero and Negative Exponents
The Zero ExponentZero at WorkNegative Means ReciprocalWriting Without NegativesPowers of TenRecap: Zero and Negative