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Grade 9:  The Learning Equation Math

11.08 Evaluating Powers

Numbers

Number Concepts

Refresher pp 16-7

 

SeekAWord2ech.class Author

Prerequisite Skills:

 

Key Terms                 

exponent, equation, variable, formula

Interactive Component Under Construction

 

 

Learning Outcomes:

The student will:

Powers, Bases and Exponents:  Grade 9 Lesson 11.04

 

 

Exponent Laws and Expressions

The following will provide additional practice. Click on the "Simplify" button.  The solution will be given in a new window.   Change the bases and/or exponents in this new window.  See if you can determine the solution before clicking the "Simplify" button again.

  • ^ refers to an exponent.  3^3 refers to 32.
  • use / to represent divide and * to represent multiply.
  • use + and - for add and subtract.
  • any letter can be used as a variable.

product law

xmxn = xm+n

 

 

Your turn, simplify the following terms involving exponents. Your final answer should only involve, at most, positive exponents. To show an exponent, we shall use a ^, so 3^2 means 32 (which we would simplify to 9).  Click on the "Help" button if you need assistance to solve a question.

source:  http://www.polaris.nova.edu/MST/online/math1030/unit6/u6s1.html

 

Review:

Power Property Example General Rule
addition 32 + 34 = 32 + 34

= 9 + 81 = 90

 xm + xn = xm + xn

Use BEDMAS to solve.
subtraction 32 - 34 = 32 - 34

= 9 - 81 = -72

 xm - xn = xm - xn

Use BEDMAS to solve.
product law 3334 = (3x3x3) (3x3x3x3)

= 33+4 = 37

 xmxn = xm+n

Keep the common base, then add the exponents.
x2x6 = (xx) (xxxxxx)

= x2+6 = x8
power of a power law (22)3 = (2x2)(2x2)(2x2)

= 22x3 =26

 (xm)n = xmn

Keep the base, then multiply  the exponents.
(x3)4 = (xxx)(xxx)(xxx)(xxx)

= x3x4 =312
power of a product law (3b)3 = (3b)(3b)(3b)

= (3x3x3)(bbb)

= 33b3

or

(3b)3 = (31b1)3 = 31x3b1x3 = 33b3

 (xy)m = xm  ym
(xy)4 = (xy)(xy)(xy)(xy)

= (xxxx)(yyyy)

= x4y4

or

(xy)4 = (x1y1)4 = x1x4y1x4 = x4y4
quotient law 35 ¸ 32 = (3x3x3x3x3)/(3x3)

= 35-2 = 33

 xm ¸ xn = xm-n

Keep the common base, then subtract the exponents.
x6 ¸ x2 = (xxxxxx)/(xx)

= x6-2 = x4
power of a quotient law (3/b)3 = (3/b)(3/b) (3/b)

= (3x3x3) /(bbb) = 27/b3

or

(3/b)3 = (31b1)3 = 31x3/b1x3)

= 33/b3 = 27/b3

 (x/y)m = xm ¸ ym
(x/y)4 =(x/y) (x/y) (x/y) (x/y)

= (xxxx) /(yyyy) = x4/y4

or

(x/y)4 = (x1/y1)4 = x1x4/y1x4 = x4/y4
negative exponents 3-4 = (1/3)4 = 1/34 x-m = (1/x)m = 1/xm
x-3 = (1/x)3 = 1/x3
1/y-4 = (y/1)4 = y4 1/x-m = xm

Working with Exponents:  Grade 8 Lesson 1101.htm

 

 

Exponent Laws

The following will provide additional practice. Click on the "Simplify" button.  The solution will be given in a new window.   Change the bases and/or exponents in this new window.  See if you can determine the solution before clicking the "Simplify" button again.

  • ^ refers to an exponent.  3^3 refers to 32.
  • use / to represent divide and * to represent multiply.
  • use + and - for add and subtract.
  • any letter can be used as a variable.

product law

xmxn = xm+n

power of a product law

(xy)m = xm  ym

power of a power law

(xm)n =xmn

quotient law

xm/ xn = xm-n

power of a quotient law

(x/y)m = xm ym

1/x-m = xm

 

Extra Practice Correction - TLE Refresher:

wpe7.jpg (43109 bytes)

(2001-2002) Click on the thumbnail on he left to see the full screen.  The correct answer shown is incorrect!!  The last 2 tiles are reversed.   The correct answer is.

wpeA.jpg (4315 bytes)

 

 

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