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Division Rules for Exponents

Division Rules for Exponents. Division Rules of Exponents Essential Questions. How do I divide powers with the same bases? How do I simplify expressions with negative and zero exponents?. x m. x 5. = x m – n. = x 5 – 3. x n. x 3. Rules and Properties. Quotient-of-Powers Property

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Division Rules for Exponents

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  1. Division Rules for Exponents

  2. Division Rules of Exponents Essential Questions How do I divide powers with the same bases? How do I simplify expressions with negative and zero exponents?

  3. xm x5 = xm – n = x5 – 3 xn x3 Rules and Properties Quotient-of-Powers Property For all nonzero real numbers x and all integers m and n, where m > n, When dividing like bases, subtract the exponents. 1. Examples: x2 =

  4. x7y3 xy 2 Examples Use the properties of exponents to simplify expressions containing fractions. Subtract the exponents for the x (7 -1= 6) 2. x6y = Subtract the exponents for the y (3 -2 = 1) Reduce the coefficients. 2x3 4x5 3. = 6x2 3 Subtract the exponent of the variables.

  5. Do These Together x6 4. = x2 x4 x3y7 5. = x2y3 xy4 x4y2z2 5x7y3z6 6. = 3 15x3yz4 10x3y4 5x2 = 7. 3 6xy4

  6. TRY THESE x8 8. = x5 x3 x4y7 9. = y5 x4y2 3x2y3z3 6x4y6z8 10. = 2x2y3z5 18x5y9 3x2y6 = 11. 2 12x3y3

  7. Zero Exponents By applying the product of powers property to the following example, we find that: Zero Property of Exponents A nonzero number to the zero power is 1: We can then divide both sides of the equation by 37 to determine the value of 30

  8. Examples Evaluate the following expressions. Solutions

  9. Negative Exponents By applying the product of powers property to the following example, we find that: We can then divide both sides of the equation by an to determine the value of a-n

  10. Rewrite the following expressions using positive exponents. Evaluate the following expressions. Solutions

  11. Evaluate the following expressions. • Rewrite the following expressions with positive exponents.

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