SIMPLIFYING MONOMIALS WITH NEGATIVE EXPONENTS

Negative Exponent Rule :

To change the negative exponent as positive, we have two ways.

(i) Change the place

(ii) Take the reciprocal.

Base with negative sign :

If base is having negative sign, we have to consider the power. 

• If the power is odd, the result will also have negative sign.
• If power is even, the result will have positive sign.

Write the expression with only positive exponents. Assume all variables represent non zero numbers. Simplify if necessary.

Problem 1 : 

4r³(r⁴)³ / 15(r³)^-2

(a) 4/15r²¹  (b)  4r²¹/15  (c)  4r⁹/15  (d)  4/15r⁹

Solution :

Problem 2 : 

(-4x⁴y^-5)³ (2x^-1y)

(a) -8x⁵/y⁶  (b)  -2x³/y⁴  (c)  -8x^-3/y⁴  (d)  -8x³y⁶

Solution :

Problem 3 : 

[(12x^-5y^-3 z⁴) / (3xy^-3z^-4)]^-1

(a) x⁴/4z⁸  (b)  x⁶/4z⁸  (c)  4x⁶/z⁸  (d)  x⁶y⁶/4z⁸

Solution :

Problem 4 : 

[(xy⁵) / (x³y)]^-2

(a) 1/x⁸ y¹²  (b)  x⁴/y⁸  (c)  1/x⁵y¹¹  (d)  y⁸/x⁴

Solution :

= [(xy⁵) / (x³y)]^-2

= [(x³y) / (xy⁵)]²

By distributing the power, we get

= [ (x³x) / (y⁵ y) ]²

= (x⁴/y⁶)²

= (x⁸/y¹²)

Problem 5 :

Which is the simplified form of (3a²b³c^-2)/(a^-1b²c)³ ?

(a) 3a⁵/b³c⁵  (b)  3ab/c⁵  (c) 3/b²c⁵  (d) 3/ab³c⁵

Solution :