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Grade 9:  The Learning Equation Math

11.05 Laws of Exponents 1

Numbers

Number Concepts

Refresher pp 10-11
 

SeekAWord2ech.class Author

Prerequisite Skills:

 

Key Terms                 

power, exponent, base, coefficient, product law, power of a product law, power of a power law

Interactive Component Under Construction

 

 

Learning Outcomes:

The student will:

 

 

 

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 power law

(xm)n =xmn

power of a product law

(xy)m = xm  ym

 

Question Generator

The following will provide additional practice. Click on the "Simplify" button.  The solution will be given in a new window.   Return to this window and click on the "Random" button. 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.
    •

Help

Click to enter an expression, then click the button.   Try to calculate the answer mentally while the answer page loads.   The Power Property rules in the chart above may be useful.  You will need to return to this page for the next random question.

 

 

 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.
    •

Powers, Bases and Exponents:  Grade 9 Lesson 11.04

 

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

 

Enrichment:

 

 

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