summary

Exponents

• Exponents define repeated multiplication.

  • Base: The number that is repeatedly multiplied.

  • Exponent: A number in superscript indicating how many times the base is multiplied by itself.

  • Example of exponents:

  • Expression: 4 imes 4 imes 4

  • Exponential representation: 4^3 (four to the power of three)

• Special Cases:

  • A number raised to the power of two is referred to as squared.

  • Example: Any number x can be represented as x^2 for squared.

  • A number raised to the power of three is called cubed.

  • Example: Any number x can be represented as x^3 for cubed.

Forms of Exponents

• There are three primary forms of exponents that can be utilized:

  1. Factored Form:

  • The base is written repeatedly with multiplication signs.

  • Example: For nine raised to the power of four:

    • Representation: 9 imes 9 imes 9 imes 9

  1. Exponential Form:

  • This form contains both the base and the exponent.

  • Example: 9^4

  1. Standard Form:

  • This is the evaluated or final solved form of the expression.

  • For instance: Calculating:

    • 9 imes 9 = 81

    • 81 imes 9 = 729

    • 729 imes 9 = 6561

    • Therefore, the standard form of 9^4 is 6561.

Square Roots

• The square root of a number is defined as a number that, when multiplied by itself, results in the original number.

  • Example: The square root of 64 is 8 since:

  • 8 imes 8 = 64

• To find the approximate square root of a number that is not a perfect square:

  • Identify the two closest perfect squares surrounding the number.

  • Use these values to estimate the square root.