Exponents lesson and worksheet
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The document discusses exponent laws and rules for manipulating exponents in mathematical expressions. It provides examples of expressing numbers with exponents, such as 49 = 72 and 625 = 53. Rules covered include the power of a power rule, (ma)b = mab, the power of a product rule, (mn)a = (ma)(na), and rules for addition, multiplication, subtraction and division of terms with the same base but different exponents. The document concludes with a worksheet that tests understanding of evaluating expressions with exponents and expressing numbers, radicals and fractional exponents according to the defined rules.
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Exponents lesson and worksheet
- 1. Angela Wang | MPM1DG Exponents ExponentLaws Square Roots as Exponents 𝑚 1 2 = √ 𝑚 NOTE: Other roots can be expressed the same way Example: 𝑚 1 3 = √ 𝑚3 𝑚 1 4 = √ 𝑚4 Expressinga Number With an Exponent Sometimes you can recognize a number as some base to some exponent. For example: 49 = 72 625 = 53 64 = 26 27 = 33 You can even express exponents in different ways For example: 47 = (22)7 = 214 492 = (72)2 = 74 (93)5 = (((33)3)5) = ((39)5) = 345 Power of a Power Rule (ma)b = mab Power of a Product Rule (mn)a = (ma)(na) Power of a Fraction Rule ( 𝑚 𝑛 )a = 𝑚 𝑎 𝑛 𝑎 Addition/Multiplication Rule m a+ b = (m a)(mb) Subtraction/Division Rule m a- b = 𝑚 𝑎 𝑚 𝑏
- 2. Angela Wang | MPM1DG Worksheet: 1. Evaluate a. 33 b. 26 c. (√27)2 d. ((2)(3))2 2. Express each of the following as a radical I a. 9 1 2 b. 13 1 4 c. 29 1 6 3. Express each of the following and 2 to the exponent of some exponent: a. 16 b. (82)12 c. ((42)3)8 d. ((((322)4)5)2)0 e. (√64)2 f. 1 Answers 1. Evaluate a. 27 b. 64 c. 27 d. 36 2. Express each of the following as a radical a. √9 b. √13 4 c. √29 6 d. √753 19 e. √ 𝑥𝑎 f. (√ 𝑎3 )2 3. Express each of the following and 2 to the exponent of some exponent: a. 24 b. 236 c. 248 d. 20 e. 26 f. 20 c. 753 1 19 d. 𝑥 1 𝑎 e. 𝑎 2 3