EXPONENTS (BASIC)(2)

EXERCISE - A

1) Find the value of:

a) 6²

b) 7³

c) 4⁴

d) 5⁵

e) 8³

f) 7⁵

2) Evaluate:

1) 2³ x 4²

2) 2² x 3³

3) 3² x 4²

4) 2³ x 5²

5) 3² x 5³

6) (4 x 3)³

7) 3³ x 5²

8) 5³ x 2⁴

9) (5 x 4)²

3) Evaluate:

a) (3/4)⁴

b) (-5/6)⁵

c) (-3/-5)³

d) (2/5)²

e) (-4/5)⁴

f) (-3/7)⁴

g) (-2/5)³

h) (1/6)⁴

i) (-1/4)⁵

j) (3/5)⁵

k) (1/-2)³

4) Evaluate:

a) (2/3)³ x (3/4)².

b) (-3/4)³ x (2/3)⁴.

5) Which is greater:

a) 2³ or 3²

b) 2⁵ or 5²

c) 4³ or 3⁴

d) 5⁴ or 4⁵

6) Express each of the following in exponential form:

a) 512.

b) 3600

c) 1250

d) 1350

e) 1458

f) 1176

g) 1/32

h) -27/125

i) 8/-512

j) 1/1024

k) 32/243

l) 16/625

7) Find the reciprocal of:

a) (-2/3)⁴

b) (3/2)⁻⁴

c) (-2/7)⁴

d) (-2/9)⁴

e) (1/2)⁻¹⁰

f) (4/7)⁻⁵

7) If a= 2 and b= 3, find the value of:

a) (a + b)².

b) (b - a)³

8) Express:

a) 1024 as power of 2.

b) 729 as a power of 3.

9) If 27 x 32 = 3ˣ x 2ʸ; find the values of x and y.

10) If 64 x 625 = 2ᵃ x 5ᵇ; find the value of (i) a and b (ii) 2ᵇ x 5ᵃ

EXERCISE - B

1) Evaluate:

a) 2⁸ ÷ 2³.

b) (3⁰)⁶ 

c) 5⁴ ÷ 5³ x 5⁵

d) 2³ ÷ 2⁸

e) 8³ x 8⁻⁵ x 8⁴

f) 4⁴ ÷ 4³ x 4⁰

g) (2⁶)⁰

h) 5⁴ x 5³ ÷ 5⁵

i) (3⁵ x 4⁷ x 5⁸)⁰

2) Simplify, giving answers with positive index:

a) i) (5/7)⁻²

    ii) (-4/7)⁻³

    iii) (7)⁻¹²

    iv) 2b⁶ . b³ , 5b⁴

b) (-a⁵)(a²)

c) (-3)²(3³)

d) (5a²b)(2ab²)(a³b)

e) 3ʸ . 3² . 3⁻⁴

f) 4x²y² ÷ 9x³y³

g) (a¹⁰)¹⁰ (1⁶)¹⁰

h) - (3ab)² (-5 a²bc⁴)²

i) (2a³)⁴ (4a²)²

j) (1/2x)³ x (6x)²

k) {(5x⁷)³ . (10x²)²}/(2x⁶)⁷

l) x²y³. 6x⁵y. 9x³y⁴

m) (-y²) (-y³)

n) (-4x) (-5x²)

o) x²ᵅ⁺⁷ . x²ᵅ⁻⁸

p) 2⁴ᵅ . 2³ᵅ . 2⁻ᵅ

q) (10²)³ (x⁸)¹²

r) (n²)² (-n²)³

s) (-2)² x (0³) x (3)³

t) (4x²y³)³ ÷ (3x²y³)³

u) (1/4ab²c)² ÷ (3/2a²bc²)⁴

v) (7p²q⁹r⁵)² (4pqr)³/(14p⁶q¹⁰r⁴)²

3) Simplify and express the answer in the positive exponent form:

a) ((-3)³ x 2⁶)/(6 x 2³)

b) -128/2187

c) {(2³)⁵ x 5⁴}/(4³ x 5²)

d) (a⁻⁷ x b⁻⁷ x c⁵ x d⁴)/(a³ x b⁻⁵ x c⁻³ x d⁸)

e) {36 x (-6)² x 3⁶}/(12³ x 3⁵)

f) (a³ b⁻⁵)⁻²

4) Evaluate:

a) 6⁻² ÷ (4⁻² x 3⁻²)

b) 5³ x 3² + (17)⁰ x 7³

c) (2²)⁰ + 2⁻⁴ ÷ 2⁻⁶ + (1/2)⁻³

d) [(5/6)² x 9/4)] ÷ [(-3/2)² x 125/216]

e) 2⁵ x 15⁰ + (-3)³ - (2/7)⁻²

f) 5ⁿ x 25ⁿ⁻¹ ÷ (5ⁿ⁻¹ x 25)ⁿ⁻¹)

5) If m= -2 and n= 2; find the value of:

a) m² + n² - 2mn.

b) 6m⁻³ + 4n².

c) mⁿ + nᵐ

d) 2n³ - 3m

6) State true or false 

a) 8 x 8¹⁵ = 64¹⁶

b) 27⁰ = 54903⁰

c) - 1ⁿ = -1, if n is an odd whole number.

d) (-3)⁻³ = +9

e) 16⁸ ÷ 4² = 4⁶

f) (-1)ⁿ = ¹, if n is an even whole number 

g) 4⁻⁴ = -16

EXERCISE - C

1) Evaluate:

a) (3/2)⁵ x (3/2)⁷

b) 8¹¹ x 8⁻¹³ x 8²

c) (-7/5)⁴ x (-7/5)⁶ x (-7/5).

d) (5/3)⁴ x (5/3)⁶ ÷ (5/3)⁴

2) Simplify:

a) {(-3/4)²}⁻³

b) [{(-2/3)²}⁻³]⁻¹

c) [{4/5}⁻⁸]¹⁾⁴

d) [(2/5)³ x (2/5)⁴ x (2/5)¹¹ ÷ (2/5)⁸]

3) Find the value of n, if (-2)³ⁿ⁺¹ x (-2)⁴= (-2)⁸.

4) Find 3³+ 4³ + 5³ and give the answer in cube.

5) If (x⁵ . x⁻²)²= 64  what is the value of x⁻⁴ ?

6) Find the value of a²b³ when a= 2 and b = 3.

7) Find the value of (2/3)⁻² + (1/3)⁻² + (1/2)⁻⁵.

8) By what number should (3)⁻⁸ be multiplied to get (3)⁻⁴ ?

9) By what number should (4)⁻⁵ be multiplied to get (4)¹² ?

10) By what number should (-3/2)⁻³ be divided so that the quotient is (4/5)⁻².

11) By what number should (2)⁻⁴ be multiplied to get 2²⁷ ?

12) Verify that: (x . y)ᵐ = xᵐ . yᵐ for x= 2, y= 3 and m= 4

EXERCISE - D

Evaluate:

1) 2⁻⁵

2) (1/4)⁻⁵

3) (-2/7)⁻⁴

4) (2/5)⁻⁴ x (2/5)⁴

5) (1/7)⁵ x (2/3)⁴ x (1/7)⁻⁸

6) (3)⁻⁶ x (6)⁶ x 27 x (8)⁻²

7) (3⁵ ÷ 3⁸)⁵ x 3⁶.

8) {(-3/2)²}⁻³

9) (1/2)⁻² + (1/3)⁻² + (1/4)⁻²

10) {(216)²⁾³}¹⁾²

11) 9³⁾² - 3 x 5⁰ - (1/81)⁻¹⁾²

12) ((3²)³ + (2/3)⁰ + 3⁵ x (1/3)⁴

13) (4⁻³ x 9⁻⁵ x b⁻⁴)/(4⁻⁵ x a⁻⁸ x b³)

14) (49 x t⁻⁵)/(7⁻³ x 10 x t⁻⁹)

15) If 27ʸ = 9/3ʸ, then find y.

16) If (5ⁿ x 5³ x 5⁻²)/5⁻⁵ = 5¹² then find n.

17) Find the value of n if 25pⁿ⁻³ = 1

18) Find the value of n if 7ⁿ = 343.

EXERCISE - E

1) Simplify:

a) 2²⁾³ x 2¹⁾³.

b) 3⁵⁾⁶ x 3²⁾³.

c) 4²⁾⁵ x 4⁻²⁾⁵.

d) 3¹⁾³/3¹⁾⁶.

e) 4⁶⁾⁷/4²⁾³.

f) 7¹⁾⁴/7¹⁾⁵.

g) 2¹⁾⁴ x 3¹⁾⁴.

h) 3⁵⁾⁸ x 5⁵⁾⁸.

i) 7²⁾³ x 3²⁾³.

j) (5³)¹⁾³.

k) (7¹⁾³)⁴.

l) (3¹⁾⁵)¹⁰.

m) 7¹⁾² x 7¹⁾³.

n) 11¹⁾²/11¹⁾⁴.

o) 7¹⁾² x 8¹⁾².

p) (3³)²⁾³.

2) Evaluate:

a) (36)¹⁾²

b) (27)¹⁾³

c) (32)¹⁾⁵.

d) (81)³⁾⁴.

e) (243)³⁾⁵.

f) (16)⁵⁾⁴.

g) (27)⁻¹⁾³.

h) (512)⁻¹⁾⁹.

i) (625)⁻³⁾⁴.

j) (27/64)⁻²⁾³.

k) (64/125)⁻²⁾³.

l) (81/16)⁻³⁾⁴.

m) (64)¹⁾⁶.

n) (81)⁻¹⁾⁴.

o) (256/625)⁻¹⁾⁴.

3) If a= 2 and b= 3, find the value of the following:

a) (aᵇ + bᵃ)⁻¹

b) (aᵃ + bᵇ)⁻¹.

4) Simplify:

a) {(243)³⁾⁵ x (25)³⁾²}/{(625)¹⁾² x (8)⁴⁾³ x (16)⁵⁾⁴}.

b) (3⁴⁰ + 3³⁹)/(3⁴¹ - 3⁴⁰).

c) 27⁻¹⁾³(27¹⁾³ - 27²⁾³).

d) (2¹⁾² x 3¹⁾³ x 4¹⁾⁴)/(10⁻¹⁾⁵ x 5³⁾⁵) ÷ (3⁴⁾³ x 5⁻⁷⁾⁵)/(4⁻³⁾⁵ x 6).

e) 3/(625)⁻¹⁾⁴ + 2/(343)⁻²⁾³ + 4/(243)⁻¹⁾⁵.

f) (64/125)⁻²⁾³ + 1/(256/625)¹⁾⁴ + √25/³√64.

g) (1³ + 2³ + 3³)¹⁾².

h) (5¹⁾³ x 25¹⁾³ x 125²⁾³)/625¹⁾².

i) (2/3)⁴(8/3)⁻¹²(32/3)⁶.

j) [{(81)¹⁾²}¹⁾⁴]².

k) 4/(216)⁻²⁾³  - 1/(256)⁻³⁾⁴.

l) {(2⁻¹ x 3²)/(2² x 3⁻⁴)}⁷⁾² x {(2⁻² x 3³)/(2³ x 3⁻⁵)}⁻⁵⁾² 

5) Find the value of p in each of the following:

a) (2³)⁴ = (2²)ᵖ.

b) 27ᵖ = 9/3ᵖ.

c) 5ᵖ⁻⁴ x 2ᵖ⁻⁵ = 5.

d) (3/5)ᵖ (5/3)²ᵖ= 125/27.

6) Find the values of x if (2/3)ˣ(3/2)²ˣ= 81/16