**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".

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