Multiplication of Monomials

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Presentation transcript:

Multiplication of Monomials Chapter 7.2

Recall when a number is raised to a power the number is the base and the exponent is the power. 23: 2 is the base and 3 is the exponent. Variables can be raised to powers also. x5 : x is the base and 5 is the exponent.

Rule for Multiplying exponential Expressions If m and n are integers then, (xm)(xn)= x(m+n)

Examples with one Variable (x2)( x3)= x(2+3) = x5 (x4 )( x5)= x(4+5) = x9 (x)( x7)= x(1+7) = x8 If a variable does not have an exponent it is assumed to be raised to the power of 1.

Examples With Numerous Variables (3x2 )(6x3) = (3)(6)(x2 x3)=18 x(2+3) = 18x5 (-3xy2)(-4x2y3) =(-3)(-4)(xx2)(y2y3)) =12x3 y5 (-x2y3)(11x9) =(-1)(11)(x2 x9)(y3) = -11x11y3

Simplify Monomials Raised to Powers. Rule for simplifying Powers of Exponential Expressions. (xm)n = xmn ; Just multiply the exponents. Rule for simplifying Powers of Products. (xmyn)p = xmp ynp Just multiply the exponents.

Examples of Exponential Powers x2*5 = x10 2. (x2y5)5 = x2*5y5*5 = x10 y25 3. (3x2y5)3 = (3)3 (x2)3( y5)3 = 27 x6y15

Examples: Recall PEMDAS 1. (-2x) (-3xy2)3 = (-2x)(-3)3 (x)3 (y2)3 = (-2)(-27) (xx3) (y6) = 54x4 y6 2. (3x) (2x2y2)3 =(3x) (2)3(x2)3(y2)3 = (3*8)(xx6)(y6) = 24x7 y6

YOU TRY! 1. (x9)5 2. (x2)15 3. (x2y8)5 4. (4x2y3)3 5. (3xy2)(-2x2y5)5

Answers 1. x45 2. x30 3. x10 y40 4. 64x6y9 5. -96x11y27 6. -32x12y10