# EXPONENT RULES WORKSHEET

Problem 1 :

Simplify :

2m2  2m3

Problem 2 :

Simplify :

m4  2m-3

Problem 3 :

Simplify :

(4a3)2

Problem 4 :

Simplify :

(x3)0

Problem 5 :

Simplify :

(12a3b2) / (3a4b3)

Problem 6 :

Simplify :

(x2y-1)4

Problem 7 :

If a-1/2  =  5, then find the value of a.

Problem 8 :

If 42n + 3  =  8n + 5, then find the value of n.

Problem 9 :

If 2x / 2y  =  23, then find the value x in terms of y.

Problem 10 :

If ax = b, by = c and  cz = a, then find the value of xyz. ## Solutions

Problem 1 :

Simplify :

2m2  2m3

Solution :

2m2  2m3  =  4m(2+3)

2m2  2m3  =  4m5

Problem 2 :

Simplify :

m4  2m-3

Solution :

m4  2m-3  =  2m(4 - 3)

m4  2m-3  =  2m1

m4  2m-3  =  2m

Problem 3 :

Simplify :

(4a3)2

Solution :

(4a3) =  42(a3)2

(4a3)2  =  16a(3)(2)

(4a3)2  =  16a6

Problem 4 :

Simplify :

(x3)0

Solution :

(x3) =  1

Problem 5 :

Simplify :

(12a3b2) / (3a4b3)

Solution :

(12a3b2) / (3a4b3)  =  (12/3)a3-4b2-3

(12a3b2) / (3a4b3)  =  4a-1b-1

(12a3b2) / (3a4b3)  =  4 / (a1b1)

(12a3b2) / (3a4b3)  =  4 / (ab)

Problem 6 :

Simplify :

(x2y-1)4

Solution :

(x2y-1)4  =  (x2)4(y-1)4

(x2y-1)4  =  x8y-4

(x2y-1)4  =  xy4

Problem 7 :

If a-1/2  =  5, then find the value of a.

Solution :

a-1/2  =  5

a  =  5-2/1

a  =  5-2

a  =  1/52

a  =  1/25

Problem 8 :

If 42n + 3  =  8n + 5, then find the value of n.

Solution :

42n + 3  =  8n + 5

(22)2n + 3  =  (23)n + 5

22(2n + 3)  =  23(n + 5)

Equate the exponents.

2(2n + 3)  =  3(n + 5)

4n + 6  =  3n + 15

n  =  9

Problem 9 :

If 2x / 2y  =  23, then find the value x in terms of y.

Solution :

2x / 2y  =  23

2x - y  =  23

x - y  =  3

x  =  y + 3

Problem 10 :

If ax = b, by = c and  cz = a, then find the value of xyz.

Solution :

Let

ax  =  b -----(1)

by  =  c -----(2)

cz  =  a -----(3)

Substitute a  =  cin (1).

(1)-----> (cz)x  =  b

czx  =  b

Substitute c  =  by.

(by)zx  =  b

bxyz  =  b

bxyz  =  b1

xyz  =  1 Apart from the stuff given in this section if you need any other stuff in math, please use our google custom search here.

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