Unit 11: Roots, exponents, & scientific notation

The number in front of the exponent is called:

the BASE

Negatives with exponent:

-a negative number will become positive with an ___ exponent and stay negative with an ___ exponent

become +: EVEN exponent

stay -: ODD exponent

Square Root:

A number which when multiplied by itself equals another number

Fractional Exponent Rule:

top goes with x

Root of decimals and exponents:

-separate fractions inside of the Square root

ex. Sqrt(49/31) —>

ex. Sqrt(49/31) —> Sqrt(49)/ Sqrt (81) —> 7/9

Square Root of a negative number is ___

Undefined (no real numbers) —> imaginary

Base to the power of 0=

1

Taking the Square roots of both sides of an equation changes the = sign to ___

Plus or Minus sign

-when square rooting, it must be with an even index

-ex. normal Sqrt has an index of 2 —> x^(1/2)

Negative exponent in denominator —> Negative Property of Exponent

ex. 1/(b^-n) —>

ex. 1/(b^-n) —> bⁿ

Multiplication and division w/ Powers of 10:

ex. (-6×10^-1)/ (-3×10^-2)

—don’t shy away from breaking the equation apart

ex. (-6×10^-1)/ (-3×10^-2) —> -6/1 *10^-1/1 * 1/-3 × 1/10^-2

^—> -6/-3 *10^-1/10^-2 —> -1-(-2)=1 or (10^-1) *(10²) —>1

—> 2× 10^1 = 20

Scientific Notation:

-count the number of values behind the ___ and count number of ___ in given number

-Coefficient must be:

ex. 96,470,000 (must end in 0)

-count the number of values behind the decimal and count number of zeros in given number

-Coefficient must be: >1 and <10

ex. 96,470,000 (4 zeros) and 9.647 (3 behind decimal)

=9.647×10⁷