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Name________________________________ Date __________ Mr. Tallman Math 8R Do Now Write the following expressions in simplest exponential form. 1) 83 ∙ 83 2) 35 3) 7−6 31 Write the following expressions in standard form. 4) 320 5) 84 ∙ 82 6) 131 Lesson #10 – Rules of Exponents Part 2 Consider the following example… Example 1) What is (32 )4 in simplest exponential form? What is the base of the exponent? ___________________________ How many times is the base being multiplied? ________________________ What is the exponent in expanded form? ________________________________________________ Using our exponent multiplication property, what is (32 )4 in simplest exponential form? ___________ **Rule: When you are raising a power to a power, you keep the base and MULTIPLY the exponents.** Example 2) What is (83 )6 in simplest exponential form? Example 3) Which shows (22 )−2 in standard form? A) 0 B) C) 2−8 1 16 D) 2−12 Here’s a quick recap of all of our exponent rules… Rule Product of Powers When you multiply two numbers with the same base, you keep the base and add the exponents. Quotient of Powers When you divide two numbers with the same base, you keep the base and subtract the exponents. Power of a Power When an exponent is raised to another power, you keep the base and multiply the exponents. Power of Zero Any number with a zero as the exponent is equal to 1. Power of One Any number with a 1 as the exponent is equal to itself. Negative Exponents If an exponent is negative, you take the reciprocal of the exponential number and make the exponent positive. Now, You Try! 4) Write (73 )6 in simplest exponential form. 5) Write (22 )3 in standard form. Example 23 ∙ 25 = 23+5 = 28 310 = 310−2 = 38 32 (64 )5 = 64×5 = 620 50 = 1 71 = 7 3−2 = 1 32 6) Write 53 ∙ 55 ∙ 51 in simplest exponential form. 7) Which of the following is not equivalent to 4−2? A) 1 B) 42 C) -16 1 16 1 1 D) ∙ 4 4 8) Write 9 8 ∙ 94 92 in simplest exponential form. 9) True or False: The number (83 )0 is equal to 1. ______________________________ 10) True or False: The number 171 is equal to 17. _____________________________ 11) Determine whether each expression shown below is equivalent to a whole number or a fraction. Write the expression in the correct box. 13 Fraction 7−3 50 31 8−2 Whole Number