 # Negative Exponents SWBAT express powers with negative exponents as decimals; express decimals as powers with negative exponents; simplify expressions with.

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Negative Exponents SWBAT express powers with negative exponents as decimals; express decimals as powers with negative exponents; simplify expressions with negative exponents

Exponents What does an exponent mean (what are you doing when you solve an exponent)? What does an exponent mean (what are you doing when you solve an exponent)? –Repeatedly multiplying the base number Discuss with a partner: What do you think you would do if you had a negative exponent? Discuss with a partner: What do you think you would do if you had a negative exponent? –Repeatedly dividing How do we rewrite negative exponents as a positive one? How do we rewrite negative exponents as a positive one? –Write it as a fraction x -y = 1/x y

Examples Write as a fraction, and a power of 10 Write as a fraction, and a power of 10 0.01 0.01 0.00001 0.00001 0.001 0.001

Examples Evaluate Evaluate 4 -1 4 -1 6 -2 6 -2 8 -3 8 -3 1/9 -3 1/9 -3

Review When we multiply exponents with the same base what do we do? When we multiply exponents with the same base what do we do? –Keep the base and add the exponent When we divide exponents with the same base what do we do? When we divide exponents with the same base what do we do? –Keep the base and subtract the exponent

Examples 7 -2 x 7 -2 7 -2 x 7 -2 2 -5 x 2 -1 2 -5 x 2 -1 (4 -1 )(4 -2 ) (4 -1 )(4 -2 ) _10 -9 _ _10 -9 _ 10 -4 10 -4 _8 0 _ _8 0 _ 8 -2 8 -2

Do the try these problems on your paper 3 -1 3 -1 –1/3 4 -3 4 -3 –1/4 3 –1/64 10 -7 10 -7 –1/10 7 –1/10000000 10 -8 10 -8 –1/10 8 0.000001 0.000001 –10 -6 0.01 0.01 –10 -2 2 -5 (2 -3 ) 2 -5 (2 -3 ) –2 -8 –1/2 8 –1/256 3 -4 (3 -2 ) 3 -4 (3 -2 ) –3 -6 –1/3 6 _11 -7 _ _11 -7 _ 11 -6 11 -6 –11 -1 –1/11 –1/2 5 _5 -6 _ _5 -6 _ 5 -2 5 -2 –5 -4 –1/5 4 3 -7 _ 3 -7 _ 3 -3 3 -3 –3 -4 –1/3 4 2 -10 _ 2 -10 _ 2 -5 2 -5 –2 -5 –1/2 5

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