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Understanding Exponents: Basics of Squared, Cubed, and Special Powers

This resource provides an introductory overview of exponents in algebra and geometry. It explains the concept of a number that indicates how many times to multiply the base. Learn about squared and cubed values, as well as the special cases of powers 0 and 1. This guide also covers how to write and evaluate expressions with exponents, including handling negative bases with and without parentheses, and the significance of even and odd exponents. Ideal for students seeking to grasp fundamental exponent rules.

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Understanding Exponents: Basics of Squared, Cubed, and Special Powers

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Presentation Transcript

  1. Warm Up • 3 x 2 • 32

  2. Exponents Intro to Algebra/Geometry

  3. Exponents A number that tells us how many times to use the base in a multiplication problem.

  4. Squared, Cubed, Powers • Squared – Exponent is 2 Multiply the base by itself • Cubed – Exponent is 3 Multiply the base by itself twice. (Use the base 3 times)

  5. Write with exponents • a x a x a x a x a x a • 3 x 3 x 3 x 3 • y x y

  6. Square Each Number • 7 • 10 • a • (1/3)

  7. Cube Each Number • 3 • a • x • 4

  8. Expand and Evaluate • 25 • 34 • 106

  9. Special Powers 0 & 1 Anything to the power of 0 = 1 Anything to the power of 1 = the base

  10. -3² & (-3)² Are these answers different? What are the steps we take when there is a negative sign?

  11. -3² When the negative sign is used with no parenthesis: • take the base to the exponent • the answer will be negative.

  12. (-3)² When the negative sign is inside parenthesis • take the negative number multiplied by itself however many times the power tells us. • If the exponent is even, the answer is positive. • If the exponent is odd, then the answer is negative.

  13. Examples • -5² 2. -4³ 3. (-5)² 4. (-1)13 5. (-3)4 6. -7²

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