**Powers of monomials :**

When we have power raised to another power for any monomial, then we have to multiply both the powers.

In case we have negative power then we have to take the reciprocal of the given term and change negative power as positive.

In case we have two monomials which are multiplying or dividing then we have to consider the power as common for both terms.

The above rule is not applicable if two or more monomials which are adding and subtracting.

**Example 1 :**

Simplify (6 t^6)^2

**Solution :**

** = (6 t^6)^2**

**Here the power 2 is common for both 6 and t^6.Since it is multiplying, we have to distribute the power for both terms. **

** = 6^2 (t^6)^2**

** = 36 t^(6 x 2)**

** = 36 t^12**

**Example 2 :**

Simplify (2 / u)^5

**Solution :**

= (2 / u)^5

**Here the power 5 is common for both numerator and denominator.**** **

** ** = (2^5 / u^5)

** ** = (32 / u^5)

** = 36 t^12**

**Example 3 :**

Simplify (5c^7)^2

**Solution :**

= (5c^7)^2

**Here the power 2 is common for both 5 and c^7**

** = 5^2 (c^7)^2**

** = (5 x 5)[ c^(7 x 2) ]**

** = 25 c^14**

**Example 4 :**

Simplify (10 t^3)^2

**Solution :**

= (10 t^3)^2

**Here the power 2 is common for both 10 and t^3**

** = **10^2 (t^3)^2

** = (10 x 10)[ t^(3 x 2) ]**

** = 100 t^6**

**Example 5 :**

Simplify (1.5 u^3)^4

**Solution :**

= 1.5^4 (u^3)^4

**Here the power 4 is common for both 1.5 and u^3**

** = 1.5**^4 (u^3)^4

** = (1.5 x 1.5 x 1.5 x 1.5)[ u^(3 x 4) ]**

** = (1.5 x 1.5 x 1.5 x 1.5)[ u^(3 x 4) ]**

** = 5.0625 u^12**

**Example 6 :**

Simplify (5/u^3)^(-4)

**Solution :**

**Since we have negative power, we have to take the reciprocal and change the negative power as positive.**

** = (u^3/5)^4**

** = (u^3)^4 / 5^4 **

** = [ u^(3x4) / 5^4 ]**

** = u^12 / 625 **

After having gone through the stuff given above, we hope that the students would have understood "Powers of monomials".

Apart from the stuff given above, if you want to know more about "Powers of monomials", 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...

**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**

**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**