# EXPONENTS AND POWERS

## What is exponents ?

The exponents of a number says how many times to use the number in a multiplication.

for example 5³ = 5 x 5 x 5

In words 5³ could be called as 5 to the power 3 or 5 cube.

 10² is called as 10 to the power 2 or simply called as 10 square. 10³ is called as 10 to the power 3 or simply called as 10 cube. If we have 1/2 in the power, we can simply write the base inside the radical or square root.If we have 1/3 in the power,we can simply write the base inside the cube root

## How to move an exponents or powers to the other side ?

 If the power goes from one side of equal sign to the other side, it will flip.that is x = 4²

## What is exponent and power?

The other names of exponent are index and power.

## Basic Rules of Exponents and powers

 Rule 1: When we have to simplify two or more the terms which are multiplying with the same base,then we have to put the same base and add the powers. Rule 2: Whenever we have two terms which are diving with the same base,we have to put only one base and we have to subtract the powers. Rule 3: Rule 4: Anything to the power zero is 1. Rule 5: If we have same power for 2 or more terms which are multiplying or dividing then we have to distribute the powers which are multiplying or dividing inside the bracket.Note :This rule is not applicable when two are more terms which are adding and subtracting.For example (x + y) ^m = (x^m + y^m) is not correct

Other things:

Point 1 :

If we don't have any number in the power then we have to consider that there is 1

Point 2 :

In case we have negative power for any fraction and if we want to make it as positive,we can write the power as positive and we should write its reciprocal only. For example

Question 1 :

Simplify 4 x ^(-1)/x^(-1/3)

Solution :

 Question 2 :Find the value of 2(256) ^(-1/8)Solution :             = 2 (2^8)^(-1/8)             = 2 (2^-1)             = 2/2             = 1

Question 3 :

Find the value of

Question 4 :

Find the value of x^(a - b) x^(b - c) x^(c - a)

Solution :

Question 5 :

Find the value of (8/27)^(-1/3) (32/243)^(-1/5)

Solution :

After having gone through the stuff given above, we hope that the students would have understood "Exponents and powers".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

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