Properties of Exponents Part 2 Learn zero exponents

Focus 11 - Learning Goal: The student will be able to work with integer

Notice what occurs when you divide powers with the same base. 5 5 55

Dividing Powers with the Same Base Divide. Write the quotient as one power. A.

Try This: Divide. Write the quotient as one power. A. 99 92 99 –

When the numerator and denominator have the same base and exponent, subtracting the exponents

Helpful Hint 00 does not exist because 00 represents a quotient of the form

THE ZERO POWER Words Numbers The zero power of any number except 0 equals

Power of Quotient Property Distribute power across the ( ). a b 2 3

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Properties of Exponents – Part 2 Learn zero exponents and division properties of exponents.

Focus 11 - Learning Goal: The student will be able to work with integer exponents. 4 3 2 1 0 In addition to 3, student will be able to go above and beyond by applying what they know about working with integer exponents. The student will be able to work with integer exponents. - Know and apply the properties of exponents. - Simplify numerical expressions with exponents. - Perform operations with scientific notation. With no help the student has a partial understanding of integer exponents. - Is able to use scientific notation to estimate very large or very small numbers. - Interpret scientific notation generated by technology. With help, the student may have a partial understanding of how to work with integer exponents. Even with help, the student is unable to work with integer exponents.

Notice what occurs when you divide powers with the same base. 5 5 55 2 = 5 • 5 = = = 5 5 5 53 DIVIDING POWERS WITH THE SAME BASE Words To divide powers with the same base, keep the base and subtract the exponents. Numbers 6 9 = 69 – 4 = 6 5 64 Algebra b m = bm – n bn

Dividing Powers with the Same Base Divide. Write the quotient as one power. A. 5 7 3 7 75 – 3 7 Subtract exponents. 2 10 B. x 9 x x 10 – 9 x Subtract exponents. Think: x 1 = x

Try This: Divide. Write the quotient as one power. A. 99 92 99 – 2 97 B. Subtract exponents. e 10 e 5 e 10 – 5 5 e Subtract exponents.

When the numerator and denominator have the same base and exponent, subtracting the exponents results in a 0 exponent. 2 4 2 – 2 = 40 = 1= 4 42 This result can be confirmed by writing out the factors. 42 42 (4 • 4) = 1 =1 = = (4 • 4) 1 (4 • 4)

Helpful Hint 00 does not exist because 00 represents a quotient of the form 0 n. 0 n But the denominator of this quotient is 0, which is impossible, since you cannot divide by 0! It is undefined!

THE ZERO POWER Words Numbers The zero power of any number except 0 equals 1. 1000 = 1 (– 7)0 = 1 Algebra a = 1, if a 0

Power of Quotient Property Distribute power across the ( ). a b 2 3 m m a = m b 2 = 22 32 =4 9

Practice! 1. 2. x 6 3 2 m 4 = x 3 63 = x 3 216 4 = 2 4 m 4 44 = 16 m 4 256