**Understanding exponents :**

Exponent says that how many times do we have to multiply the base by itself.

For example, let us consider

2³ = 2 x 2 x 2 (we multiply the base "2" three times)

Before going to see example based on the above concept, we have to know about two terms

(i) Base

(ii) Exponent (or) power (or) index

**How to read ?**

We have to read the above question as 5 raised to the power 3, (or) 5 cube.

**Example 1 :**

Write the number 128 as the power of 2

**Solution :**

To write the number 128 as the power of 2, we have to split the number 128 using 2 times table.

128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

Since 2 is repeating 7 times, we have to write 2⁷.

**Rule 1:**

**When we have to simplify two or more the terms which are multiplying with 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 :**

Whenever we have power to the power, we have to multiply both powers.

**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,we have to apply the powers for every terms.

**Exponents with negative powers**

Whenever we have a negative number as exponent and we need to make it as positive,we have to flip the base that is write the reciprocal of the base and we can change the negative exponent as positive exponent.

Let us see some examples based on the above concepts.

**Example 2 :**

If 2^p = 32, find the value of p.

**Solution :**

To find the value of which is in he power, we have to write the number 32 as the multiples of 2.

2^p = 2 x 2 x 2 x 2 x 2

Since 2 is repeating five times, we have to write 2 x 2 x 2 x 2 x 2 as 2^5

2^p = 2⁵

Since the bases are equal, we can say the powers are also equal.

p = 5

**Example 3 :**

Simplify (2 x 3)⁴

**Solution :**

(2 x 3)⁴ = 6⁴

Since the power is 4, we have to multiply 6 four times.

= 6 x 6 x 6 x 6

= 1296

**Example 4 :**

**Solution :**

[(2/8)^2x] x [(2/8)^x] = [(2/8)^6]

(2/8)^(2x + x) = (2/8)^6

(2/8)^(3x) = (2/8)^6

Since the bases are equal on both sides, we can equal the powers.

3x = 6

x = 6/3

x = 2

**Example 5 :**

Simplify

**Solution :**

Combining the terms which are having same base.

After having gone through the stuff given above, we hope that the students would have understood "Understanding exponents".

Apart from the stuff given above, if you want to know more about "Understanding exponents", please click here

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

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**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**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**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 **

**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 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**