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Multiplication of Monomials

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. 2 3 : 2 is the base and 3 is the exponent. Variables can be raised to powers also. x 5 : x is the base and 5 is the exponent.

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Multiplication of Monomials

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  1. Multiplication of Monomials Chapter 7.2

  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.

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

  4. 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.

  5. 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

  6. 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.

  7. Examples of Exponential Powers • 1. (x2)5 = • x2*5 = x10 • 2. (x2y5)5 = • x2*5y5*5 = x10 y25 • 3. (3x2y5)3 = • (3)3 (x2)3(y5)3 = 27 x6y15

  8. 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

  9. YOU TRY! • 1. (x9)5 • 2. (x2)15 • 3. (x2y8)5 • 4. (4x2y3)3 • 5. (3xy2)(-2x2y5)5 • 6. (-x2) (2x2 y2)5

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

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