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Powers Notice: You must multiply the coefficients (#s in frontof the powers). -3am •2an = -6am+n Multiplying Powers am •an = am+n Simplify the following problems COMPLETELY! Before you begin, remember... (Don't pick any answer with these exponents!) You cannot leave your final answer with any zero or negative exponents! You should not see the same variable more than once. To multiply powers with the same base, Pick: add, subtract, multiply, or divide you must write the base and the exponents x2 x3 x4 . . . x-1 = x x-3 = x x5 = x = 2n . 4n = 6n 6n2 8n 8n2 15y6 8y6 5y . 3y6 = 15y7 8y7 Drag the correct answers to the blocks. 3t4 -3t2 3t3 -3t4 . . . . -2t2 = 2t-2 = -2t-2 = 2t = -6t6 ? -6t5 ? -6t ? -6 ? 9x2 • 2x-2 18x 18 18 18x-4 x4 -3t3 • -2t 6t4 -5t4 6t3 5t3 7n6(3n5) 10n30 21n30 10n11 21n11 -5z3• 7z4 -35z7 -35z12 35z12 2z7 2xy4 • x6y2 2x6y6 2x7y6 2x6y8 2x7y8 4a0• 5a3•-2a5 -40 -40a9 -20a8 -40a8 -4k2 • 7k-1 -28 k 28 k2 -28k 1 28k 6mn-4 • m5n2 6m5n-2 6m6n2 6m5 6m6 n2 n2 a-3b2 • a-4b-1 a12b a-7b a12 b a7 b2 -b3c • 5b-4c 5c -5c2 b7 b -5c2 c2 5b b7 9m4n-3p • -m2n3p-5 -9m6n m6n0 9p4 p4 -9m8 -9m6 p5 p4 Simplify 3-3 1/27 1/9 -1/27 -27 Simplify x-2 1/x2 -x2 -1/x2 x2 Simplify 50 0 1 5 1/5 Simplify -40 -4 4 1 -1 Simplify (-2)0 1 -1 2 -2 Simplify m-5 m5 -m5 1/m5 -1/m5 Simplify 4t-3 -1/4t3 -4t3 1/4t3 4/t3 Simplify (3m)-2 3/m2 9/m2 1/9m2 -1/9m2 Simplify (5k)0 1 5k 5 1/5k (Power) (am)n = amn Raising Powers to Powers Power (write the base, multiply the exponents) Simplify. Make sure you have no zero or negative exponents in your answers! Don't forget to raise your coefficients to the power, too!Ex: (2m3)3 = 23 • (m3)3 = 8m9 When raising a power to a power, __________the exponents add multiply subtract divide you must (x2)3 x6 x5 x8 x1 (3t5)3 9t15 27t15 3t15 27t8 (b-2)-5 b-7 b-10 b7 b10 (5w-2)2 25w-4 25 w4 5w4 1 25w4 Remember: x = x1 Dividing Powers Simplify each problem completely! (no zero or negative exponents!) (variable does not appear twice!) (Subtract the exponents!) (with the same base) Make sure you divide the coefficients! am an = a(m-n) m-1 m2 x3 x = m = x g g-4 g3 g-3 g5 1 g5 a3b2 a5b2 a2b4 a15b4 a2b0 a2 x6y7 x2y 1 x4 x4y6 y6 x12y7 1 x4y7 m 1 m9 m5 m-4 m9 1 m 25xy3 20y4 5 5xy-1 y2 5xy4 5y4 The voice inside your head that says that you can't do this, is a LIAR! -9a-1b4 -3 3 3ab-4 -3b8 -3 a2b8 a2 8m5n2 n 4m2n 2 m3n2 4m3 1 1 2m3n 2m3 simplify: 7mp2 mp2 7n6 n3 21mn2p-1 3m2n-4p m3p2 7m n2p2 7n6 4x8y-5 20x3 5x5y-2 x5 x5 x11y8 5y8 5x2 5 Solve: 32x - 2 = 35x + 7 x = |