4 1 Exponents Warm Up Problem of the

4 -1 Exponents Warm Up Problem of the Day Lesson Presentation Course 33

4 -1 Exponents Warm Up Find the product. 1. 5 • 5 • 5 625 2. 3 • 3 27 3. (– 7) • (– 7) – 343 4. 9 • 9 Course 3 81

4 -1 Exponents Problem of the Day What two positive integers when multiplied together also equal the sum of the same two numbers? 2 and 2 Course 3

4 -1 Exponents Learn to evaluate expressions with exponents. Course 3

4 -1 Exponents Vocabulary exponential form exponent base power Course 3

4 -1 Exponents If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. Both 27 and 33 represent the same power. Exponent Base 2 Course 3 7

4 -1 Exponents Additional Example 1: Writing Exponents Write in exponential form. A. 4 • 4 • 4 • 4 = 44 Identify how many times 4 is a factor. B. (– 6) • (– 6) = (– 6)3 Identify how many times – 6 is a factor. Reading Math Read –(63) as “-6 to the 3 rd power” or “-6 cubed”. Course 3

4 -1 Exponents Additional Example 1: Writing Exponents Write in exponential form. C. 5 • 5 • d • d = 5 2 d 4 Course 3 Identify how many times 5 and d are used as a factor.

4 -1 Exponents Check It Out: Example 1 Write in exponential form. A. x • x • x= x 5 Identify how many times x is a factor. B. d • d • d = d 3 Course 3 Identify how many times d is a factor.

4 -1 Exponents Check It Out: Example 1 Write in exponential form. C. 7 • b • b 2 7 • b • b=7 b Course 3 2 Identify how many times 7 and b are used as a factor.

4 -1 Exponents Additional Example 2: Evaluating Powers Evaluate. Find the product of five 3’s. A. 35 35 = 3 • 3 • 3 = 243 B. (– 3)5 Find the product of five – 3’s. (– 3)5 = (– 3) • (– 3) = – 243 Helpful Hint Always use parentheses to raise a negative number to a power. Course 3

4 -1 Exponents Additional Example 2: Evaluating Powers Evaluate. C. (– 4)4 = (– 4) • (– 4) = 256 D. 28 28 = 2 • 2 • 2 = 256 Course 3 Find the product of four – 4’s. Find the product of eight 2’s.

4 -1 Exponents Check It Out: Example 2 Evaluate. Find the product of four 7’s. A. 74 74 = 7 • 7 • 7 = 2401 B. (– 9)3 Find the product of three – 9’s. (– 9)3 = (– 9) • (– 9) = – 729 Course 3

4 -1 Exponents Check It Out: Example 2 Evaluate. C. –(5)2 = –(5) • (5) = – 25 D. 97 97 = 9 • 9 • 9 • 9 = 4, 782, 969 Course 3 Find the product of two 5’s and then make the answer negative. Find the product of seven 9’s.

4 -1 Exponents Additional Example 3: Using the Order of Operations Evaluate x(yx – zy) + xy for x = 4, y = 2, and z = 3. x(yx – zy) + xy = 4(24 – 32) + 42 Substitute 4 for x, 2 for y, and 3 for z. = 4(16 – 9) + 16 Evaluate the exponent. = 4(7) + 16 Subtract inside the parentheses. = 28 + 16 Multiply from left to right. = 44 Add. Course 3

4 -1 Exponents Check It Out: Example 3 Evaluate z – 7(2 x – xy) for x = 5, y = 2, and z = 60. z – 7(2 x – xy) = 60 – 7(25 – 52) Substitute 5 for x, 2 for y, and 60 for z. = 60 – 7(32 – 25) Evaluate the exponent. = 60 – 7(7) Subtract inside the parentheses. = 60 – 49 Multiply from left to right. = 11 Subtract. Course 3

4 -1 Exponents Additional Example 4: Geometry Application 1 2 Use the formula (n 2 – 3 n) to find the number of diagonals in a 7 -sided figure. 1 2 1 2 1 2 (n 2 – 3 n) (72 – 3 • 7) Substitute the number of sides for n. (49 – 3 • 7) Evaluate the exponent. (49 – 21) Multiply inside the parentheses. (28) Subtract inside the parentheses. 14 diagonals Course 3 Multiply

4 -1 Exponents Additional Example 4 Continued A 7 -sided figure has 14 diagonals. You can verify your answer by sketching the diagonals. Course 3

4 -1 Exponents Check It Out: Example 4 1 2 Use the formula (n 2 – 3 n) to find the number of diagonals in a 4 -sided figure. 1 2 1 2 1 2 (n 2 – 3 n) (42 – 3 • 4) Substitute the number of sides for n. (16 – 3 • 4) Evaluate the exponents. (16 – 12) Multiply inside the parentheses. (4) Subtract inside the parentheses. 2 diagonals Course 3 Multiply.

4 -1 Exponents Check It Out: Example 4 Continued A 4 -sided figure has 2 diagonals. You can verify your answer by sketching the diagonals. Course 3

4 -1 Exponents Lesson Quiz: Part I Write in exponential form. 1. n • n • n n 4 2. (– 8) • (h) (– 8)3 h 3. Evaluate (– 4)4 256 4. Evaluate x – 213 Course 3 • z – yx for x = 5, y = 3, and z = 6.

4 -1 Exponents Lesson Quiz: Part II 5. A population of bacteria doubles in size every minute. The number of bacteria after 5 minutes is 15 25. How many are there after 5 minutes? 480 Course 3