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Grade 9:  The Learning Equation Math

11.04:  Powers, Bases and Exponents

 Number Concepts Refresher pp 8-9

 Interactive Component Under Construction

Learning Outcomes

The student will:

## Exponential Expression Calculator

Click on to get the value of 32.

Enter the exponent and base, then click on to calculate other powers.    The exponent on this calculator must be less than 600.

 Enter the Exponent: Enter the Base: ( ) =

Note:  00 = indeterminate.  The answer shown for 00 on this calculator is incorrect.

Source:  Web Winder JavaScript Calculators

 Exponential Form Other Expanded Form(s)/Repeated Multiplication(s) Other Exponential Form(s) 45 = (22)5 22 x 22 x 22 x 22 x 22 22+2+2+2+2 = 210 84 = (23)4 23 x 23 x 23 x 23 23+3+3+3 = 212 93 = (32)3 32 x 32 x 32 32+2+2 = 36 163 = (42)3 = (24)3 42 x 42 x 42 (42)3 = 42x3 = 46 (24) x (24) x (24) (24)3 = 44x3 = 412 252 = (52)2 52 x 52 52+2 = 54 273 = (33)3 33 x 33 x 33 33+3+3 = 39

## Rational Numbers and Variables

 Power Coefficient Base Exponent 3.3x4 3.3 x 4 2/3a3 2/3 a 3 -2.5n2 -2.5 n 2 4.5z or  4.5z1 4.5 z 1 x -2 1 x -2

p r 2 is an example where an irrational numbers (p) is used as a coefficient.

Powers can be expressed using rational numbers and variables as bases and/or coefficients.  If there is no operation sign (+, -, x, /), it is understood the operation is multiplication.

4 x t x t x t x t = 4tttt

 Exponential Form (Power) Expanded Form/Repeated Multiplication Simplified Expression 3n5 3 x n x n x n x n x n or 3nnnnn Cannot be simplified. 2.5r3 2.5rrr Cannot be simplified (2/3r)4 (2/3r)(2/3r)(2/3r)(2/3r) 16/81r4 (-2/3r)4 (-2/3r)(-2/3r)(-2/3r)(-2/3r) 16/81r4 -(2/3r)4 -(2/3r)(2/3r)(2/3r)(2/3r) -16/81r4

## Scientific Calculator

Press Reload/Refresh if calculator does not function.
Follow the directions to learn how to convert from scientific notation to whole numbers using the scientific calculator, then make your own examples.
-54 = - ( 5 ) = -625
(-5)4 = 5   = 625
- (-5)4 5 = -625
(-5)0 5 = 1
00 Note:   00 = indeterminate.  The answer shown for 00 on this calculator is incorrect.
 Exponential Form (Power) Expanded Form/Repeated Multiplication -3m6 -3mmmmmm 2.5x2 2.5xx (1/3k)5 (1/3k)(1/3k)(1/3k)(1/3k)(1/3k) (-1/3p)5 (-1/3p)(-1/3p)(-1/3p)(-1/3p)(-1/3p) -(1/3b)5 -(1/3b)(1/3b)(1/3b)(1/3b)(1/3b)

## Question Generator

• ^ 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.

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.

Number of Ancestors 1000 Years Ago

## Problem Solving Steps

2.  Make a plan including the problem solving strategy
3.  Solve the problem.
4.  Look back.

## Problem Solving Strategies

sequence the operations
use a flow chart
use a table
look for a pattern
guess and check
solve a simpler problem (break into parts)
work backward
interpret graphs
use a diagram/sketch
use a formula
make assumptions
use a data bank
use logic

Optional resources:

Curriculum Support for Math- Problem Solving Part 2

Problem Solving Strategies

### Sequencing the Operation

1.  List the facts.
2.  Decide on the solution order.
3.  Make the calculation.

### Use a Flow Chart

1.  Use a flow chart to represent the problem.
2.  Solve the problem.

### Use a Table

1.  Organize the data in the table.
2.  Complete the table if necessary.
3.  Find the answer from the table.

### Look for a Pattern

1.  Study the information you are given on the graph.
2.  Determine what you are to find.
3.  Determine if you need an approximate or exact answer.

### Guess and Check

1.  Study the problem and guess the answer.
3.  If necessary guess and check again.

### Solve a Simpler Problem (Break into Parts)

1.  Break the problem into smaller problems.
2.  Solve the problem.

### Interpret Graphs

1.  Study the information you are given on the graph.
2.  Determine what you are to find.
3.  Determine if you need an approximate or exact answer.

### Use a Diagram/Sketch

1.  Study the information you are given on the graph.
2.  Determine what you are to find.
3.  Determine if you need an approximate or exact answer.

### Use a Formula

1.  Write the formula.
2.  Substitute variables with know values.
3.  Calculate for the remaining variable.

### Make Assumptions

1.  Study the information you are given on the graph.
2.  Determine what you are to find.

### Use a Data Bank

1.  Look up the information you need.
2.  Solve the problem.

### Use Logic/Reasoning

1.  Organize the data.
2.  Interpret the data to find the answer.

## Powers Review

Powers are calculated by multiplying the base by itself the number of times indicated by the exponent.  As multiplication is to repeated addition, powers are to repeated multiplication.

power = baseexponent = base^exponent

Special names are used for exponent two and three.

base2 =base x base = base^2 = base squared

base3 = base x base x base = base^3 = base cubed

 Concept/Term Example(s) Definition/Explanation power 81 is the fourth power of 3, because:3 x 3 x 3 x 3 = 81 34 is another way of writing this power the answer from multiplying a number by itself one or more times.A power has two parts: baseexponent = 34  and can be written/read in several ways: the fourth power of three three exponent four three to the fourth power 32 33 Exponents 2 and 3 can also be written/read another way: 32  is read three squared 33  is read three cubed base In 34 , the base is 3. the number being multiplied in a power exponent In 34 , the exponent is 4. the number of times a number is being multiplied by itself in a power coefficient In 5x2, the coefficient is 5. the constant (number) multiplier of the variables in a term

 Exponential Form (Power) Expanded Form/Repeated Multiplication Standard Form (Standard Name) 34 3 x 3 x 3 x 3 81 33 3 x 3 x 3 27 32 3 x 3 9 31 3 3 30 no expanded form 1

Note:  The standard name of any non-zero base with an exponent of zero is equal to 1.

Enrichment:

Powers of x

Exponents - contains review and enrichment

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