EXPONENTS

EXPONENTIAL NOTATION X IS THE BASE 2 IS THE EXPONENT OR POWER

EXPONENTIAL NOTATION THE BASE IS SQUARED

EXPONENTIAL NOTATION EXPONENT IS THE NUMBER OF TIMES THE BASE IS MULTIPLIED BY ITSELF

EXPONENTIAL NOTATION Y IS THE BASE 8 IS THE EXPONENT

EXPONENTIAL NOTATION Y IS THE BASE 8 IS THE EXPONENT

Compare these two cases 6 IS THE BASE (THE NEG. SIGN IS NOT PART OF THE BASE, IT MUST REMAIN PART OF THE ANSWER) -6 IS THE BASE

EXPONENTIAL NOTATION WHAT IS THE BASE? WHAT WILL BE SQUARED?

EXPONENTIAL NOTATION WHAT IS THE BASE? -h is the base

EXPONENTIAL NOTATION WHAT IS THE BASE? What will be raised to the 5th power?

EXPONENTIAL NOTATION WHAT IS THE BASE? r will be raised to the 5th power

TRY THESE

EVALUATING EXPRESSIONS WITH EXPONENTS

Evaluating Expression with Exponents Evaluate 2x 2 (x+y) When x=6 & y=3

Evaluating Expression with Exponents Evaluate 2x 2 (x+y) When x=6 & y=3 1.Put in x & y values 2x 2 (x+y) = 2(6) 2 (6+3)

Evaluating Expression with Exponents Evaluate 2x 2 (x+y) When x=6 & y=3 1.Put in x & y values 2.Use PEMDAS 2x 2 (x+y) = 2(6) 2 (6+3) = 2(6) 2 (9) = 2(36)9 = 729 = 648

MULTIPLYING SIMILAR BASES X X2X2 X

THE RULE IS TO ADD THE EXPONENTS

MULTIPLYING SIMILAR BASES

TRY THESE PROBLEMS

DIVIDING SIMILAR BASES

THE RULE IS TO SUBTRACT THE EXPONENT OF THE DENOMINATOR FROM THE EXPONENT OF THE NUMERATOR

DIVIDING SIMILAR BASES THE RULE IS TO SUBTRACT THE EXPONENTS

TRY THESE

NEGATIVE EXPONENTS You can change a negative exponent to positive by switching it’s base from numerator to denominator or vice versa.

NEGATIVE EXPONENTS MOVE THE BASE & EXPONENT FROM THE NUMERATOR TO THE DENOMINATOR OR VICE VERSA AND CHANGE THE SIGN OF THE EXPONENT

NEGATIVE EXPONENTS X 2 /X 2 IS WHAT PROPERTY?

MULTIPLY NUMERATORS & MULTIPLY DENOMINATORS NEGATIVE EXPONENTS

ANYTHING TO THE ZERO POWER IS EQUAL TO ? NEGATIVE EXPONENTS

Why is anything to the zero power equal to 1?

Check Out These Patterns

Or For Anything

THIS IS WHY SWITCHING A NEGATIVE EXPONENT CHANGES ITS SIGN

Let’s compare the Neg. Exponent Rule with the Dividing Fraction Rule To divide fractions you INVERT THE 2ND FRACTION AND CHANGE THE DIVISION SIGN TO MULTIPICATION For negative exponents you INVERT THE BASE WITH AND CHANGE THE SIGN OF THE EXPONENT

Try These

What if the negative exponent is in the denominator? The same rule of inverting the base with the exponent and making the exponent positive applies but let see why this is so.

What if the negative exponent is in the denominator? Use the Multiplicative Identity to Simplify

What if the negative exponent is in the denominator? Do you remember what x 0 is equal to?

What if the negative exponent is in the denominator? INVERT AND CHANGE EXPONENT SIGN

Try These

Try These ANSWERS

SUMMARY SO FAR DIVIDING EXPONENTS SUBTRACT THE EXPONENT OF THE DENOMINATOR FROM THE EXPONENT OF THE NUMERATOR MULTIPLYING EXPONENTS ADD THE EXPONENTS INVERTING A NEGATIVE EXPONENT CHANGES ITS SIGN

DON’T BE MARY TO THE Z POWER GET WITH IT!

POWER TO A POWER THIS IS A POWERFUL IDEA

POWER TO A POWER VS. MULT. SIMILAR BASES

POWER TO A POWER MULTIPLY THE EXPONENTS

POWER TO A POWER Express Answers as Positive Exponents

POWER TO A POWER

COMPARING MULTIPLY SIMILAR BASES & POWER TO A POWER

WHAT’S THE DIFFERENCE?

NOTHING REALLY (A MONOMIAL IS A PRODUCT) A monomial is a term with a number and one or more variables (letters) raised to some power. Examples are:

Let’s take a close look at DISTRIBUTING THE POWER

Simplify (4d 5 ) 2 Power of a Monomial

Simplify (4d 5 ) 2 = 4 12 d 52 = 4 2 d 10 1.Multiply the outside power to the inside powers. Power of a Monomial

Simplify (4d 5 ) 2 = 4 12 d 52 = 4 2 d 10 = 16 d 10 1.Multiply the outside power to the inside powers. 2.Simplify Power of a Monomial

Simplify (2x 3 y 4 ) 5 1.Multiply the outside power to the inside powers. 2.Simplify

Power of a Monomial Simplify (2x 3 y 4 ) 5 = 2 15 x 35 y 45 = 2 5 x 15 y 20 or 32 x 15 y 20 1.Multiply the outside power to the inside powers. 2.Simplify

Take a Power of a Quotient Simplify

Take a Power of a Quotient Simplify 1.Multiply the outside power to the inside powers.

Take a Power of a Quotient Simplify 1.Multiply the outside power to the inside powers. 2.Simplify

Mult/Divide Monomials with Exponents

1.Multiply the numbers 2.Multiply the Similar Variables by adding the exponents.

Mult/Divide Monomials with Exponents 1.Multiply the numbers 2.Multiply the Similar Variables by adding the exponents. 3.Simplify

5 Exponent Rules 1.When multiplying similar bases add exponents 2.When dividing similar bases subtract exponents 3.When inverting change exponents’ sign 4.When taking a power of a power multiply exponents 5.When taking a power of a product or quotient distribute the outside power to the inside powers

DIVIDING EXPONENTS SUBTRACT THE EXPONENTS MULTIPLYING EXPONENTS ADD THE EXPONENTS Anything to the zero power equals 1 EXPONENTS (Or POWERS are REPEATED MULTIPICATION