POWERS AND EXPONENTS

A power is the result of a repeated multiplication of the same factor. 

For example, 125 is 5 to the 3rd power. Because

125  =  5 ⋅ 5 ⋅ 5

A power can be written in a form that has two parts. 

A number called the base and a number called the exponent. The exponent shows the number of times the base is used a factor. 

Number raised to the first power, such as 131, are usually written without the exponent. 

We can read and write powers as given below. 

Power

In words

Value

151

15 to the first power

151 = 15

(0.4)2

0.4 to the second power, or 0.4 squared

(0.4)(0.4) = 0.16

43

4 to the third power, or 4 cubed

⋅ 4 ⋅ 4 = 64

74

7 to the fourth power

⋅ 7 ⋅ 7 ⋅ 7 = 2401

Using Exponents

Example 1 : 

Write the following products using an exponent. 

a.  15 ⋅ 15 ⋅ 15 ⋅ 15 

b.  (0.5)(0.5)(0.5) 

c.  x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x

d.  y ⋅ y ⋅ y ⋅ y ⋅ y

Solution : 

a.  154

The base 15 is used as a factor 4 times. 

b.  (0.5)3

The base 0.5 is used as a factor 3 times. 

c.  x6

The base x is used as a factor 6 times. 

d.  y5

The base y is used as a factor 5 times. 

Example 2 : 

Evaluate the expression m5 when m = 3. 

Solution : 

=  m5

Substitute 3 for m.

=   (3)5

Use 3 as a factor 5 times. 

=  3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3

Multiply. 

=  243

Example 3 : 

Evaluate the expression x4 when x = 0.5. 

Solution : 

=  x4

Substitute 0.5 for x.

=   (0.5)4

Use 0.5 as a factor 4 times. 

=   (0.5)(0.5)(0.5)(0.5)

Multiply. 

=  0.0625

Use Powers in Formulas

Example 4 : 

An artist uses a cube-shaped block of ice to make an ice sculpture for a competition. Find the volume of the block of ice. 

Solution : 

Use the formula for volume of a cube :

V  =  s3

Substitute 15 for s. 

=  153

Use 15 as a factor 3 times. 

=  15 ⋅ 15 ⋅ 15

Multiply. 

=  3375

The volume of the block of ice is 3375 cubic inches.  

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ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

Quantitative aptitude

Multiplication tricks

APTITUDE TESTS ONLINE

Aptitude test online

ACT MATH ONLINE TEST

Test - I

Test - II

TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

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Reflection through x -axis

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Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices

ORDER OF OPERATIONS

BODMAS Rule

PEMDAS Rule

WORKSHEETS

Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

SOHCAHTOA

Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem

MENSURATION

Mensuration formulas

Area and perimeter

Volume

GEOMETRY

Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem

ANALYTICAL GEOMETRY

Analytical geometry formulas

Distance between two points

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Point of intersection

Slope of the line 

Perpendicular distance

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Parabola

CALCULATORS

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MATH FOR KIDS

Missing addend 

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LIFE MATHEMATICS

Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

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Unitary method time and work

SYMMETRY

Order of rotational symmetry

Order of rotational symmetry of a circle

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Lines of symmetry

CONVERSIONS

Converting metric units

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WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

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Word problems on direct variation and inverse variation 

Word problems on unit price

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Converting metric units word problems

Word problems on simple interest

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Percentage word problems 

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Decimal word problems

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Word problems on mixed fractrions

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Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6