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Chapter 8.1 Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems Students will know how to apply the laws of exponents when multiplying monomials. Example 1Simplify: x2 * x3 Remember: x2 = x * x which can also be written as xx x2 = x * x and x3 = x * x * x Therefore x2 * x3 = (x*x)*(x*x*x) = xx * xxx = xxxxx There are 5 x’s in the answer Therefore x2 * x3 = x5 Rule: When multiplying monomials you must add the exponents together. Xm * xn = xm+n 1. 33 * 34 2. x3 * x4 3. x5(x3) 4. x7(x-2) 1. 33 * 34 37 2. x3 * x4 x7 3. x5(x3) x8 4. x7(x-2) x5 Example 2Simplify (2x3)(3x4) Multiply the numbers together first: 2 * 3 = 6 Multiply the variables together second: x3 * x4 = x7 Put the numbers and letters back together for your answer: 6x7 Rule: When multiplying monomials you multiply the numbers and letter separately 1. 3x3 * 4x2 2. 5x4(2x3) 3. -2x2(4x) 4. -7x(-3x3) 1. 3x3 * 4x2 12x5 2. 5x4(2x3) 10x7 3. -2x2(4x) -8x3 4. -7x(-3x3) 21x4 Example 3Simplify (-2x2y3)(3x5y2) Multiply the numbers together first: –2 * 3 = -6 Multiply the x’s separately: x2 * x5 = x7 Multiply the y’s separately: y3 * y2 = y5 1. 3x3y2 * 4x2y2 12x5y4 2. 5x4y3(2x3y4) 10x7y7 3. -2x2y2(4xy) -8x3y3 4. -7xy(-3x3y3) 21x4y4 Example 4 Simplify (x3)2 Remember, (x3)2 = (x3) * (x3) = xxx * xxx Therefore (x3)2 = x6 Rule: When a monomial with an exponent is then raised to an exponent you multiply the exponents together. (Xm)n = xm*n You can always write out x3 twice and add the exponents 1. (x2)3 2. (x4)4 3. (x3)7 1. (x2)3 x6 2. (x4)4 x16 3. (x3)7 x21 Example 5 Simplify: 2x2(3x3)2 Remember order of operations, exponents come before multiplication! Also, any number squared means to multiply it by itself Therefore: 2x2(3x3)(3x3) Multiply the numbers: 2 * 3 * 3 = 18 Multiply the variables: x2 * x3 * x3 = x8 Put the numbers and letters back together: 18x8 1. 2x2(3x3)2 2. (4x3)2(2x5) 3. (3x4)3(2x3)2 1. 2x2(3x3)2 2. (4x3)2(2x5) 3. (3x4)3(2x3)2 108x18 18x8 32x11 1. 2. 3. 4. 5. x2 * x3 3x(2x3) -2x3(4x4) (x4)3 2x3(3x4)2 5 x * 3x(2x3) 6x4 -2x3(4x4) -8x7 12 4 3 x (x ) 2x3(3x4)2 18x11 1. x2 2. 3. 4. 5. x3