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Published byClifton Thompson Modified over 9 years ago
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Essential Question: What is the first step for simplifying an exponential expression that contains negative exponents?
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1) Zero as an exponent Any number to the 0 power equals 1 Why? ▪ x 3 = 1x 1x 1x ▪ x 7 = 1x 1x 1x 1x 1x 1x 1x ▪ x 0 = no “x”s, so we leave just a “1” 2) Negative exponents Any number to a negative exponent moves the base to the opposite side of a fraction, and the exponent becomes positive
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Simplify: 4 -3 Negative exponent. Move the base. Make the exponent positive.
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Simplifying Expressions Simplify 4y 0 x -3 Exponent of 0 = 1 Move negative exponent Make exponent positive
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Y OUR T URN – Simplify each expression 3 -4 -7 0 11m -5
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Multiplying Same Bases (add) When two numbers are multiplied together and have the same base, their exponents are added. Why? ▪ x 3 = x x x ▪ x 5 = x x x x x ▪ x 3 x 5 = x x x x x x x x = x 8 ▪ x 3 x 5 = x 3+5 = x 8
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Dividing Same Bases (subtract) When two numbers are divided and have the same base, their exponents are subtracted. Why? ▪ x 3 = x x x ▪ x 5 = x x x x x ▪
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Power to a power (multiply) If an exponent is raised to a power (typically outside a parenthesis), multiply the exponents together. Examples: ▪ (3x 2 y 3 ) 4 = 3 4 x 8 y 12 = 81x 8 y 12 ▪
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Y OUR T URN – Simplify each expression (7a 2 )(-2a -5 )
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Assignment Page 368 1 – 24 (all)
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