2 6 Exponents Learn to evaluate expressions with

2 -6 Exponents The term 27 is called a power. If a number is

2 -6 Exponents Example 1 A & 1 B: Writing Exponents Write in exponential

2 -6 Exponents Example 1 C & 1 D: Writing Exponents Write in exponential

2 -6 Exponents Example 2 A & 2 B: Evaluating Powers Evaluate. Find the

2 -6 Exponents Example 2 C & 2 D: Evaluating Powers Continued Evaluate. C.

2 -6 Exponents Try This: Example 1 A & 1 B Write in exponential

2 -6 Exponents Try This: Example 1 C & 1 D Write in exponential

2 -6 Exponents Try This: Example 2 A & 2 B Evaluate. Find the

2 -6 Exponents Try This: Example 2 C & 2 D Evaluate. Find the

2 -6 Exponents Example 3: Simplifying Expressions Containing Powers Simplify (25 – 32) +

2 -6 Exponents Try This: Example 3 Simplify (32 – 82) + 2 •

2 -6 Exponents Example 4: Geometry Application 1 2 Use the formula (n 2

2 -6 Exponents Try This: Example 4 Continued Verify your answer by sketching the

2 -6 Exponents Additional Example 4 Continued Verify your answer by sketching the diagonals.

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2 -6 Exponents Learn to evaluate expressions with exponents. Pre-Algebra

2 -6 Exponents The term 27 is called a power. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. Exponent Base 2 Pre-Algebra 7

2 -6 Exponents Example 1 A & 1 B: Writing Exponents Write in exponential form. A. 4 • 4 • 4 • 4 = 44 Identify how many times 4 is a factor. B. d • d • d = d 5 Identify how many times d is a factor. Reading Math Read 44 as “ 4 to the 4 th power. ” Pre-Algebra

2 -6 Exponents Example 1 C & 1 D: Writing Exponents Write in exponential form. C. (– 6) • (– 6) = (– 6)3 Identify how many times – 6 is a factor. D. 5 • 5 = 52 Identify how many times 5 is a factor. Pre-Algebra

2 -6 Exponents Example 2 A & 2 B: 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. Pre-Algebra

2 -6 Exponents Example 2 C & 2 D: Evaluating Powers Continued Evaluate. C. (– 4)4 Find the product of four – 4’s. (– 4)4 = (– 4) • (– 4) = 256 D. 28 Find the product of eight 2’s. 28 = 2 • 2 • 2 = 256 Pre-Algebra

2 -6 Exponents Try This: Example 1 A & 1 B Write in exponential form. A. x • x • x = x 5 Identify how many times x is a factor. B. d • d • d = d 3 Pre-Algebra Identify how many times d is a factor.

2 -6 Exponents Try This: Example 1 C & 1 D Write in exponential form. C. (– 3) • (– 3) • (– 3) = (– 3)4 D. 7 • 7 = 72 Pre-Algebra Identify how many times 3 is a factor. Identify how many times 7 is a factor.

2 -6 Exponents Try This: Example 2 A & 2 B 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 Pre-Algebra

2 -6 Exponents Try This: Example 2 C & 2 D Evaluate. Find the product of two – 5’s. C. (– 5)2 = (– 5) • (– 5) = 25 Find the product of seven 9’s. D. 97 97 = 9 • 9 • 9 • 9 = 4, 782, 969 Pre-Algebra

2 -6 Exponents Example 3: Simplifying Expressions Containing Powers Simplify (25 – 32) + 6(4). = (32 – 9) + 6(4) Evaluate the exponents. = (23) + 6(4) Subtract inside the parentheses. = 23 + 24 Multiply from left to right. = 47 Add from left to right. Pre-Algebra

2 -6 Exponents Try This: Example 3 Simplify (32 – 82) + 2 • 3. = (9 – 64) + 2 • 3 Evaluate the exponents. = (– 55) + 2 • 3 Subtract inside the parentheses. = – 55 + 6 Multiply from left to right. = – 49 Add from left to right. Pre-Algebra

2 -6 Exponents Example 4: Geometry Application 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 Pre-Algebra Multiply

2 -6 Exponents Try This: Example 4 Continued Verify your answer by sketching the diagonals. 2 diagonals Pre-Algebra

2 -6 Exponents 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 Pre-Algebra Multiply

2 -6 Exponents Additional Example 4 Continued Verify your answer by sketching the diagonals. 14 Diagonals Pre-Algebra