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

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Evaluating Algebraic Expressions 4-1Exponents Vocabulary exponential form exponent base power

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Evaluating Algebraic Expressions 4-1Exponents 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. 27 and 3 3 are equivalent. 7 Exponent Base 2

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

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

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Evaluating Algebraic Expressions 4-1Exponents Identify how many times x is a factor. x x x x x = x 5 Write in exponential form. Check It Out! Example 1 A. x x x x x Identify how many times d is a factor. d d d = d 3 B. d d d

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Evaluating Algebraic Expressions 4-1Exponents Identify how many times 7 and b are each used as a factor. 7 7 b b = 7 2 b 2 Check It Out! Example 1 C. 7 7 b b Write in exponential form.

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Evaluating Algebraic Expressions 4-1Exponents A. 3 5 = 243 3 5 = 3 3 3 3 3Find the product. B. Simplify. Additional Example 2: Simplifying Powers = 1 27

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Evaluating Algebraic Expressions 4-1Exponents D. – 2 8 = 256 –2 8 = –(2 2 2 2 2 2 2 2) = –256 = (–4) (–4) (–4) (–4) (–4) 4 C. (–4) 4 Simplify. Additional Example 2: Simplifying Powers Find the product. Find the product. Then make the answer negative.

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Evaluating Algebraic Expressions 4-1Exponents The expression (–4) 4 is not the same as the expression –4 4. Think of –4 4 as –1 ● 4 4. By the order of operations, you must evaluate the exponent before multiplying by –1. Caution!

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Evaluating Algebraic Expressions 4-1Exponents A. 7 4 = 2401 7 4 = 7 7 7 7 Find the product. Simplify. Check It Out! Example 2 Find the product. B. = 1818

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Evaluating Algebraic Expressions 4-1Exponents D. – 9 4 = 25 –9 4 = –(9 9 9 9) = –6,561 = (–5) ( – 5) (–5) 2 C. (–5) 2 Evaluate. Find the product. Find the product. Then make the answer negative. Check It Out! Example 2

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Evaluating Algebraic Expressions 4-1Exponents Additional Example 3: Using the Order of Operations 4(7) + 16 Substitute 4 for x, 2 for y, and 3 for z. Simplify the powers. Subtract inside the parentheses. Multiply from left to right. 4(2 4 – 3 2 ) + 4 2 4(16 – 9) + 16 28 + 16 Evaluate x(y x – z y ) + x for x = 4, y = 2, and z = 3. y x(y x – z y ) + x y Add. 44

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Evaluating Algebraic Expressions 4-1Exponents Check It Out! Example 3 60 – 7(7) Substitute 5 for x, 2 for y, and 60 for z. Simplify the powers. Subtract inside the parentheses. Multiply from left to right. 60 – 7(2 5 – 5 2 ) 60 – 7(32 – 25) 60 – 49 Evaluate z – 7(2 x – x y ) for x = 5, y = 2, and z = 60. z – 7(2 x – x y ) Subtract. 11

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Evaluating Algebraic Expressions 4-1Exponents (7 2 – 3 7) 1212 Additional Example 4: Geometry Application Simplify inside the parentheses. Multiply. Substitute the number of sides for n. Subtract inside the parentheses. 14 diagonals (49 – 21) 1212 (n 2 – 3n) 1212 (28) 1212 Use the expression (n 2 – 3n) to find the number of diagonals in a 7-sided figure. 1212

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

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Evaluating Algebraic Expressions 4-1Exponents (4 2 – 3 4) 1212 Check It Out! Example 4 Simplify inside the parentheses. Multiply Substitute the number of sides for n. Subtract inside the parentheses. 2 diagonals (16 – 12) 1212 (n 2 – 3n) 1212 (4) 1212 Use the expression (n 2 – 3n) to find the number of diagonals in a 4-sided figure. 1212

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Evaluating Algebraic Expressions 4-1Exponents A 4-sided figure has 2 diagonals. You can verify your answer by sketching the diagonals. Check It Out! Example 4 Continued

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Evaluating Algebraic Expressions 4-1Exponents Lesson Review! Write in exponential form. 1. n n n n 2. (–8) (–8) (–8) (h) 256 –213 (–8) 3 h 3. (–4) 4 5. Evaluate xz – y x for x = 5, y = 3, and z = 6. n4n4 6. A population of bacteria doubles in size every minute. The number of bacteria after 5 minutes is 15 2 5. How many are there after 5 minutes? 480 Simplify. 4.

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