Zero and Negative Exponents © 2006, Mr. C. Burke. All rights reserved

Zero and Negative Zero and Negative ExponentsExponents

© 2006, Mr. C. Burke. All rights reserved.© 2006, Mr. C. Burke. All rights reserved.

Review: Adding and Review: Adding and Subtracting ExponentsSubtracting Exponents

If you multiply two terms that have the If you multiply two terms that have the same base same base valuevalue, you , you addadd the exponents. the exponents.

xx33 * x * x66 = x = x99

If you divide two terms that have the If you divide two terms that have the same base same base valuevalue, you , you subtract subtract the exponents.the exponents.

xx88 / x / x66 = x = x22

Review: Multiplying Review: Multiplying ExponentsExponents

If you have a variable that has more than If you have a variable that has more than one exponent, you one exponent, you multiplymultiply the exponents. the exponents.

(a(a33))22= a= a33 * a * a33 = a = a3*2 3*2 = a= a66

(b(b22))33= b= b22 * b * b22 * b * b22 = b = b2*3 2*3 = b= b66


Use the Use the Distributive PropertyDistributive Property if you have more than one if you have more than one variable inside the parentheses:variable inside the parentheses:

(ab)(ab)22= a * a * b * b = a= a * a * b * b = a22bb2 2

(5c(5c44))22= 5 * 5 * c= 5 * 5 * c44 * c * c44 = 25b = 25b88

(mc(mc22))33= m * m * m * c= m * m * m * c22 * c * c22 * c * c22 = m = m33cc66


Try these examples in your notebooks:Try these examples in your notebooks:

(xy)(xy)22= _____________= _____________

(jk(jk33))33= _____________= _____________

(abc)(abc)4 4 = ______________= ______________


Compare your answers. How did you do?Compare your answers. How did you do?

(xy)(xy)22= x * x * y * y = = x * x * y * y = xx22yy2 2

(jk(jk33))33= j * j* j * k= j * j* j * k33 * k * k33 * k * k33 = = jj8 8 kk88

(abc)(abc)4 4 = = a * a * a* a* b* b* b* b * c * c * c a * a * a* a* b* b* b* b * c * c * c

= = aa44bb44cc44

Zero ExponentsZero Exponents

Anything divided by itself is one. (1)Anything divided by itself is one. (1)

55 mm nn22

55 mm nn22

However, we said that when we divide, we However, we said that when we divide, we subtract exponents, so subtract exponents, so

nn22 / n / n22 = n = n2 – 2 2 – 2 = n= n00

ANY NUMBER OR EXPRESSION WITH AN ANY NUMBER OR EXPRESSION WITH AN EXPONENT OF ZERO has the value of 1.EXPONENT OF ZERO has the value of 1.

Negative ExponentsNegative Exponents

Look at the chart below:Look at the chart below:

5533 = 5 * 5 * 5 = 125 = 5 * 5 * 5 = 125

5522 = 5 * 5 = 25 = 5 * 5 = 25 (5(533 divided by 5) divided by 5)

5511 = 5 = 5 = 5 = 5 (5(522 divided by 5) divided by 5)

As we divide by 5, the exponent goes down As we divide by 5, the exponent goes down by 1. What happens if we keep this by 1. What happens if we keep this pattern going?pattern going?


Look at the chart below:Look at the chart below:

5533 = 5 * 5 * 5 = 5 * 5 * 5 = 125= 125

5522 = 5 * 5 = 5 * 5 = 25= 25

5511 = 5 = 5 = 5= 5

5500 = 1 = 1 = 1= 1

55-1-1 = 1 / 5 = 1 / 5 = 1 / 5= 1 / 5

55-2-2 = 1/ 5 * 1/ 5 = 1/ 5 * 1/ 5 = 1 / 25= 1 / 25

55-3-3 = 1/ 5 * 1/ 5 * 1/ 5 = 1/ 5 * 1/ 5 * 1/ 5 = 1 / 125= 1 / 125


Look at the pattern:Look at the pattern:

11 1 1

55-3 =-3 = nn-4 =-4 =

5533 n n44

Rewrite these expressions without Rewrite these expressions without negative exponents:negative exponents:

nn-3-3 mm-4-4pp33qq-2-2 jj–3–3

kk–4–4

HomeworkHomeworkPage 382, #1-5, #20-24Page 382, #1-5, #20-24

Please COPY the question and write the Please COPY the question and write the answer on your loose leaf paper.answer on your loose leaf paper.

Write each expression as an integer or simple Write each expression as an integer or simple fraction.fraction.

-2.57-2.5700 44-2-2 (-5)(-5)-1-1 (2/3) (2/3)-1-1 1/ 2 1/ 2-3-3

Write each expression so that it contains only Write each expression so that it contains only positive exponents.positive exponents.

1/c1/c-1-1 1/x1/x-7-7 3ab3ab00 (5x)(5x)-4-4 5 5-2-2/p/p

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Zero and Negative Exponents © 2006, Mr. C. Burke. All rights reserved