Rational Exponents Radicals Mrs Daniel Algebra 1 Exponents

Rational Exponents & Radicals Mrs. Daniel- Algebra 1

Exponents

Definition: Exponent • The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number.

The Zero Exponent Rule • Any number (excluding zero) to the zero power is always equal to one. • Examples: § 1000=1 § 1470=1 § 550 =1

Negative Power Rule •

Let’s Practice… •

The One Exponent Rule • Any number (excluding zero) to the first power is always equal to that number. • Examples: § a 1 = a § 71 = 7 § 531 = 53

The Power Rule (Powers to Powers) When an exponential expression is raised to a power, multiply the exponents. Try these… 1. (w 4)2 3. (x 3)4 2. (q 2)8

Products to Powers (ab)n = anbn Distribute the exponent/power to all variables and/or coefficients. For example: (6 y) 2 = (62)(y 2)= 36 y 2 (7 x 3)2 = (7)2(x 3)2 = 49 x 6

Let’s Practice… 1. (5 x 2)2 4. (6 x 4)2 2. (3 wk 3)3 5. (n 5)2(4 mn-2)3 3. (-2 y)4 6. (5 x 2)2

The Quotient Rule •

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Power of a Fraction •

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Untangling Exponential Expressions 1. Move expressions with negative outside exponents to bottom. 2. Distribute all outside exponents. 3. Add/Subtract to combine duplicate variables. 4. No negatives in final answer!!

Let’s Practice #1

Let’s Practice #2

Let’s Practice #3

Simplifying Radicals

Radical Vocab

How to Simplify Radicals 1. Make a factor tree of the radicand. 2. Circle all final factor pairs. 3. All circled pairs move outside the radical and become single value. 4. Multiply all values outside radical. 5. Multiply all final factors that were not circled. Place product under radical sign.

Let’s Practice… •

How to Simplify Cubed Radicals 1. Make a factor tree of the radicand. 2. Circle all final factor groups of three. 3. All circled groups of three move outside the radical and become single value. 4. Multiply all values outside radical. 5. Multiply all final factors that were not circled. Place product under radical sign.

Let’s Practice… •

Simplifying Rational Exponents

Review: Radical Vocab

How to Simplify Radicals 1. Make a factor tree of the radicand. 2. Circle all final factor “nth groups”. 3. All circled “nth group” move outside the radical and become single value. 4. Multiply all values outside radical. 5. Multiple all final factors that were not circle. Place product under radical sign.

Let’s Practice… •

Code: Fractional Exponents

Let’s Practice #1 •

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Let’s Practice #3

Applications

Rational & Irrational Numbers

Rational Numbers •

Irrational Numbers •

Let’s Practice… •

Will it be Rational or Irrational? Sums: Rational + Rational = Rational + Irrational = Irrational + Irrational = Products: Rational x Rational = Rational x Irrational = Irrational x Irrational =