# LAWS OF EXPONENTS WORKSHEET

Problem 1 :

If x-1/3 = 5/2, then find the value of x.

Problem 2 :

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

Problem 3 :

If 5x/25= 125, then solve for 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 :

In the equation 2√(x - 2) = 3√2, if x ≥ 2, then find the value of x. x-1/3 = 5/2

x = (5/2)-3/1

x = (5/2)-3

x = (2/5)3

Distribute the exponent to numerator and denominator.

x = 23 / 53

x = 8/125

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

5x/25= 125

5x/(52)= 53

5x/52= 53

5x - 2y = 53

x - 2y = 3

x = 2y + 3

ax = b

Substitute a = cz.

(cz)x = b

czx = b

Substitute c = by.

(by)zx = b

bxyz = b

bxyz = b1

xyz = 1

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)2 = 16

B : [-2(2)]2(2) = (-4)4 = 256

C : [2(2)]2 = (4)2 = 16

D : 2(2)2(2) = 2(2)4 = 2(16) = 32

So, option B is the greatest.

√(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

x3z = y9

x3z = y3(3)

x3z = (y3)3

Substitute xfor y3.

x3z = (x2)3

x3z = x6

3z = 6

Divide each side by 3.

z = 2

n4 = 20x

n⋅ n = 20x

Substitute x for n3.

⋅ n = 20x

nx = 20x

Divide each side by x.

n = 20

(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

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

4x - 8 = 18

4x = 26

Divide each side by 4.

x = 6.5

## Video Lessons

Introduction to Exponents

Laws of Exponents - 1

Laws of Exponents - 2

Laws of Exponents - 3

Laws of Exponents - 4

Important Stuff

Problem - 1

Problem - 2

Problem - 3

Problem - 4

Problem - 5

Problem - 6

Problem - 7

Problem - 8

Problem - 9

Problem - 10

Problem - 11

Problem - 12

Problem - 13

Problem - 14

Problem - 15

Problem - 16

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