# LAWS OF EXPONENTS WORKSHEET

## About "Laws of Exponents Worksheet"

Laws of Exponents Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on laws of exponents.

Before look at the worksheet, if you would like to know laws of exponents in detail,

## Laws of Exponents Worksheet - Problems

Problem 1 :

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

Problem 2 :

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

Problem 3 :

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

Problem 4 :

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

Problem 5 :

If a and b are positive even integers, which of the following is greatest ?

A)   (-2a)b

B)   (-2a)2b

C)   (2a)b

D)   2a2b

Problem 6 :

If √(x√x)   =  xa, then find the value of a.

Problem 7 :

If x2  =  y3 and x3z  =  y9, then find the value of z.

Problem 8 :

If n3   =  x, n4  =  20x and n > 0, then find the value of n.

Problem 9 :

If (√9)-7 ⋅ (√3)-4  =  3k, then find the value of k.

Problem 10 :

2√(x - 2)  =  3√2

In the equation above, if x  2, then find the value of x. ## Laws of Exponents Worksheet - Solutions

Problem 1 :

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 2 :

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 3 :

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 4 :

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  =  cz in (1).

(1)-----> (cz)x  =  b

czx  =  b

Substitute c  =  by.

(by)zx  =  b

bxyz  =  b

bxyz  =  b1

xyz  =  1

Problem 5 :

If a and b are positive even integers, which of the following is greatest ?

A)   (-2a)b

B)   (-2a)2b

C)   (2a)b

D)   2a2b

Solution :

Because a and b are positive even integers, better we can assume some values for a and b and go through each choice.

Let a  =  2 and b  =  2.

Substitute a  =  2 and b  =  2 in each option.

A ----> [-2(2)]2  =  (-4)4  =  16

B ----> [-2(2)]2(2)  =  (-4)4  =  256

C ----> [2(2)]2  =  (4)4  =  16

D ----> 2(2)2(2)  =  2(2)4  =  2(16)  =  32

So, option B is the greatest.

Problem 6 :

If √(x√x)   =  xa, then find the value of a.

Solution :

√(x√x)   =  xa

√(x ⋅ x1/2)   =  xa

√(x1 + 1/2)   =  xa

√(x3/2)   =  xa

(x3/2)1/2   =  xa

x3/4   =  xa

3/4  =  a

So, the value of a is 3/4.

Problem 7 :

If x2  =  y3 and x3z  =  y9, then find the value of z.

Solution :

x3z  =  y9

x3z  =  y⋅ 3

x3z  =  (y3)3

Substitute xfor y3.

x3z  =  (x2)3

x3z  =  x6

3z  =  6

Divide each side by 3.

z  =  2

So, the value of z is 2.

Problem 8 :

If n3   =  x, n4  =  20x and n > 0, then find the value of n.

Solution :

n4  =  20x

n⋅ n  =  20x

Substitute x for n3.

x ⋅ n  =  20x

nx  =  20x

Divide each side by x.

n  =  20

So, the value of n is 20.

Problem 9 :

If (√9)-7 ⋅ (√3)-4  =  3k, then find the value of k.

Solution :

(91/2)-7 ⋅ (31/2)-4  =  3k

(9)-7/2 ⋅ (3)-4/2  =  3k

(32)-7/2 ⋅ 3-2  =  3k

3⋅ (-7/2) ⋅ 3-2  =  3k

3-7 ⋅ 3-2  =  3k

3-7 - 2  =  3k

3-9  =  3k

k  =  -9

So, the value of k is -9.

Problem 10 :

2√(x - 2)  =  3√2

In the equation above, if x  2, then find the value of x.

Solution :

2√(x - 2)  =  3√2

Square both sides to get rid of the radicals.

[2√(x - 2)]2  =  (3√2)2

2⋅ [√(x - 2)]2  =  3⋅ (√2)2

4 ⋅ (x - 2)  =  9 ⋅ 2

Simplify.

4x - 8  =  18

Add 8 to each side.

4x  =  26

Divide each side by 4.

x  =  6.5

So, the value of x is 6.5 After having gone through the stuff given above, we hope that the students would have understood, "Laws of Exponents Worksheet".

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