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Math Notes

 

SOLVING RADICALS

EXPONENTS

 

-AN EXPONENT SHOWS HOW MANY TIMES THE BASE NUMBER IS MULTIPLIED. 

3^4 = 3x3x3x3=81

  • 3 IS THE BASE AND 4 IS THE EXPONENT.

 A FEW REMINDERS FOR EVALUATING EXPONENTS

  • A BASE WITH AN EXPONENT OF 0 EQUALS 1
  • A BASE WITH AN EXPONENT OF 1 EQUALS THE BASE NUMBER.
  • A POSITIVE BASE WITH A POSITIVE EXPONENT PRODUCES A POSITIVE NUMBER.
  • A NEGATIVE BASE WITH AN EVEN EXPONENT PRODUCES A POSITIVE NUMBER.
  • A NEGATIVE BASE WITH AN ODD EXPONENT PRODUCES A NEGATIVE NUMBER.
  • A BASE WITH A NEGATIVE EXPONENT IS WRITTEN AS ITS RECIPROCAL(FRACTION) WITH A POSITIVE EXPONENT.

RULES FOR EXPONENTS

MULTIPLY EXPONENTS 

  • ADD THE  EXPONENTS AND KEEP THE BASE THE SAME

DIVIDE EXPONENTS

  • SUBTRACT THE EXPONENTS AND KEEP THE BASE THE SAME

POWER OF A POWER

  • TO SIMPLIFY A NUMBER THAT HAS A POWER RAISED TO ANOTHER POWER, MULTIPLY THE EXPONENTS AND KEEP THE BASE THE SAME.

 

 

 

SCIENTIFIC NOTATION

3.4293 X 10^3

3.4293 IS THE COEFFICIENT AND 3 IS THE EXPONENT

TO CHANGE FROM SCIENTIFIC NOTATION TO STANDARD NOTATION

  • IF EXPONENT POSITIVE, MOVE THE DECIMAL TO THE RIGHT THAT MANY TIMES
  • IF EXPONENT NEGATIVE, MOVE THE DECIAL TO THE LEFT THAT MANY TIMES

TO CHANGE FROM STANDARD NOTATION TO SCIENTIFIC NOTATION

STEP 1:

  • IDENTIFY IF THE NUMBER IS LARGER THAN ONE OR SMALLER THAN ONE. 
  • IF NUMBER IS LARGER THAN ONE THEN YOU KNOW THE EXPONENT IS POSITIVE AND IF THE NUMBER SMALLER THAN ONE YOU KNOW THE EXPONENT IS NEGATIVE.

STEP 2:

  • FIND WHERE THE DECIMAL IS AND MOVE IT BEHIND THE FIRST NATURAL OR COUNTING NUMBER

STEP 3:

FILL IN THE EMPTY SPACES FOR THE ANSWER

______STEP 2______ X 10^_____STEP1_____

MULTIPLICATION OR DIVISION WITH SCIENTIFIC NOTATION

STEP 1:

MULTIPLY OR DIVIDE THE COEFFICIENT 

STEP 2:

APPLY EXPONENT RULES FOR MULTIPLICATION OR DIVISION

  • ADD IF ITS MULTIPLICATION AND SUBTRACT IF ITS DIVISION

STEP 3:

BRING IT ALL BACK TOGETHER AND MAKE SURE THE COEFFICIENT IS IN SCIENTIFIC NOTATION

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