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Angela Wang | MPM1DG

ExponentsExponent Laws

Square Roots as Exponentsm12 = √m

NOTE: Other roots can be expressed the same wayExample: m1

3=3√mm14=4√m

Expressing a Number With an ExponentSometimes you can recognize a number as some base to some exponent.For example:

49 = 72625 = 5364 = 2627 = 33You can even express exponents in different waysFor example:

47 = (22)7 = 214492 = (72)2 = 74(93)5 = (((33)3)5) = ((39)5) = 345

Power of a Power Rule(ma)b = mabPower of a Product Rule(mn)a = (ma)(na)Power of a Fraction Rule¿) a =

ma

na

Addition/Multiplication Rulem a + b = (m a)(m b)Subtraction/Division Rulem a - b = ma

mb


Worksheet:1. Evaluate a. 33b. 26c. (√27)2d. ((2)(3))22. Express each of the following as a radicalI a. 912b. 1314c. 29163. Express each of the following and 2 to the exponent of some exponent:a. 16b. (82)12c. ((42)3)8d. ((((322)4)5)2)0e. (√64)2f. 1

Answers1. Evaluatea. 27b. 64c. 27d. 362. Express each of the following as a radicala. √9b. 4√13c. 6√29d. 19√753e. a√ xf. ( 3√a)23. Express each of the following and 2 to the exponent of some exponent:a. 24b. 236c. 248

c. 753119d. x 1ae. a 23


d. 20e. 26f. 20