Indices Practice Set

Indices: [1 mark]

1. Find the value of (64)3/4.

2. Find the value of (243)-2/5.

3. Find the value of (x)3/4 if x = 16

4. Simplify: (a)3x-3y. (a)3y-3z. (a)3z-3x

5. Find the value of 21x7 z11รท3x3 z5 if x = 1 and z = 3.

6. Simplify: x(a-b). x(b-c). x(c-a)

7. Find the value of (a+b+c)(x+y+z) if x + y+ z = 0.

8. Find the value of (x+y+z)(x+y+z) if x + y + z = 1.

9. What should be the power of x such that its value will be 1/x7 ? 

10. What should be the power of x such that its value will be 1/x-3 ?

Answers:

1. 8

2.

3. 8

4. 1

5. 5103

6. 1

7. 1

8. (x + y + z)

9. -7

10. 3

Indices: [2 mark]

1. Find the value of: (x-y)2 . (x-y)-2.

2. Find the value of yx . zx if x = 1, y = 2 and z = 3.

3. Simplify: xa(b-c) . xb(c-a) . xc(a-b)

4. Simplify:

    \[ \frac{x^{a+b}. y^{a-b}}{x^{a-b}. y^{a+b}} \]

5. Find the value of 7x2yz if x = 1 and y = 7 and z = -1.

6. Find the value of x(a+b). y(a-b) if a = 2, b = -1, x = 3 and y = 3.

7. Find the value of ab. ac. aa if a + b + c = 0.

8. Prove that: a(x-y)(x+y). a(y-z)(y+z). a(z-x)(z+x)

9. Prove that: (p-1+q-1)2 = 25/36 if p = 2 and q = 3.

10. Prove that: p1/x. q1/y. r1/z =1 if xy + yz + zx = 0.

Answers:

1. 1

2. 6

3. 1

4. 1

5. 1

6. 81

7. 1

8. 1