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4-1 Exponents 4-1/4-2 Exponents and Integer 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 3 3 represent the same power. 7 Exponent Base 2

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4-1 Exponents Identify how many times 4 is a factor. 4 4 4 4 = 4 4 Write in exponential form. Example 1: Writing Exponents A. 4 4 4 4 Read –(6 3 ) as “negative 6 to the 3rd power” or “negative 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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4-1 Exponents Identify how many times 5 and d are used as a factor. 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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4-1 Exponents A. 3 5 = 243 3 5 = 3 3 3 3 3 Find the product of five 3’s. Always use parentheses to raise a negative number to a power. Helpful Hint Simplify. Example 2: Simplifying Powers

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4-1 Exponents = 256 = (–4) (–4) (–4) (–4) (–4) 4 B. (–4) 4 Simplify. Example 2: Simplifying Powers Find the product of four –4’s.

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4-1 Exponents Example 3: Using the Order of Operations 4(7) + 16 Substitute 4 for x, 2 for y, and 3 for z. Evaluate the exponent. 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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4-1 Exponents Look for a pattern in the table to extend what you know about exponents to include negative exponents. ÷ 10 10 2 1 0 –1 10 –2 10 100 10 1 1 1 1 = 0.1 1 10 1 100 = 0.01

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4-1 Exponents Example 1: Using a Pattern to Simplify Negative Exponents Simplify. Write in decimal form. A. 10 –2 10 –2 = 1 10 = 1 100 = 0.01 B. 10 –1 = = 0.1 1 10 = 1 Extend the pattern from the table. Multiply. Write as a decimal. Extend the pattern from the table. Multiply. Write as a decimal.

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4-1 Exponents

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4-1 Exponents 5 –3 Write the power under 1; change the sign of the exponent. Example 2: Evaluating Negative Exponents Simplify. Find the product of three ’s. 1515 Simplify.

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4-1 Exponents (–10) –3 Write the power under 1; change the sign of the exponent. Additional Example 2: Evaluating Negative Exponents Simplify. Find the product of three ’s. 1 –10 Simplify. 1 –10 –10 –10 –1000 1 = –0.001

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4-1 Exponents 4 –2 Write the reciprocal; change the sign of the exponent. Example 3 Simplify. Find the product of two ’s. 1414 Simplify. 4 1 2 1 4 16 1

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4-1 Exponents

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4-1 Exponents Evaluate 8 2 –(1 1 – 2 0 ) –2. Example 4: Zero Exponent Example

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