There are two important rules in the topic "Exponent properties with parentheses". Those are

(i) Whenever we have exponent raised by another exponent, we have to multiply those exponents.

(ii) Whenever we have common power for two or more numbers or variables which are multiplied inside the parenthesis. We have to distribute the power for those terms which are multiplied

Note:

This rule is not applicable for addition and subtraction of two terms.

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 we want to make it as positive, we can write the power as positive and we should write its reciprocal only. For example

now we have to distribute the power for both numerator and denominator. So, we will get 3²/5² =9/25

Find the value of (-5) **³**

To find the value of the above expression, first we have to consider the power.

- If the power is odd, then the answer will have negative sign.
- If the power is even, then the answer will have positive sign.

here, the power of -5 is 3, that is odd. So, the answer will have negative sign and we have to multiply the base three times.

Finally we will get -125 as the answer.

**Procedure of ****multiplying two terms with exponents**

Whenever we want to multiply two or more terms, we have to follow the below order.

(1) Symbol

(2) Number

(3) Variable

Let us see how it works

Multiply ( 5 x² ) and (-2 x³)

= ( 5 x² ) **x** (-2 x³)

= 10 x⁵

**Question 1 :**

Simplify (5x²)⁴ x (2x)³

**Solution :**

= (5x²)⁴ x (2x)³

5⁴ = 5 x 5 x 5 x 5

2³ = 2 x 2 x 2

Since x⁸ and x³ are having same base, we can combine these terms.

Let us see the next example on "Exponent properties with parentheses"

Find the value of 2(256) ^(-1/8)
= 2 (2^8)^(-1/8) = 2 (2^-1) = 2/2 = 1 |

Let us see the next example on "Exponent properties with parentheses"

**Question 3 :**

Find the value of (81 x⁴/y⁻⁸)^1/4

**Solution :**

Let us see the next example on "Exponent properties with parentheses"

**Question 4 :**

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

**Solution :**

Basic laws of exponents:

When we have to simplify two or more terms which are multiplying with same base,then we have to put the same base and add the powers.

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.

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 |

**More example problems using laws of exponents:**

Example 1 :

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

Solution :

Example 2 :

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

Solution :

After having gone through the stuff given above, we hope that the students would have understood "Let us see the next example on "Exponent properties with parentheses".

Apart from the stuff given above, if you want to know more about "Exponent properties with parentheses", please click here.

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

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM 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**

**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**