R d sharma solutions mathematics class 8 Solutions for Chapter 2 powers

Exercises in Chapter 2 powers Grade 8

Powers Exercise 2.1

Powers Exercise 2.2

Powers Exercise 2.3

Questions in Powers Exercise 2.1

Express each of the following as a rational number of the form p/q, where p and q are integers and q ≠ 0:

(i) 2-3

(ii) (-4)-2

(iii) 1/(3)-2

(iv) (1/2)-5

(v) (2/3)-2

Find the values of each of the following:

(i) 3-1 + 4-1

(ii) (30 + 4-1) × 22

(iii) (3-1 + 4-1 + 5-1)0

(iv) ((1/3)-1 – (1/4)-1)-1

Find the values of each of the following:

(i) (1/2)-1 + (1/3)-1 + (1/4)-1

(ii) (1/2)-2 + (1/3)-2 + (1/4)-2

(iii) (2-1 × 4-1) ÷ 2-2

(iv) (5-1 × 2-1) ÷ 6-1

Simplify:

(i) (4-1 × 3-1)2

(ii) (5-1 ÷ 6-1)3

(iii) (2-1 + 3-1)-1

(iv) (3-1 × 4-1)-1 × 5-1

Simplify:

(i) (32 + 22) × (1/2)3

(ii) (32 – 22) × (2/3)-3

(iii) ((1/3)-3 – (1/2)-3) ÷ (1/4)-3

(iv) (22 + 32 – 42) ÷ (3/2)2

By what number should 5-1 be multiplied so that the product may be equal to (-7)- 1?

By what number should (1/2)-1 be multiplied so that the product may be equal to (-4/7)-1?

By what number should (-15)-1 be divided so that the quotient may be equal to (- 5)-1?

Questions in Powers Exercise 2.2

Write each of the following in exponential form:

(i) $(3/2)^{-1}$ × $(3/2)^{-1}$ × $(3/2)^{-1}$ × $(3/2)^{-1}$

(ii) $(2/5)^{-2}$ × $(2/5)^{-2}$ × $(2/5)^{-2}$

Evaluate:

(i) 5-2

(ii) (-3)-2

(iii) (1/3)-4

(iv) (-1/2)-1

Express each of the following as a rational number in the form p/q:

(i) 6-1

(ii) (-7)-1

(iii) (1/4)-1

(iv) (-4)-1 × (-3/2)-1

(v) (3/5)-1 × (5/2)-1

Simplify:

(i) (4-1 × 3-1) 2

(ii) (5-1 ÷ 6-1) 3

(iii) (2-1 + 3-1) -1

(iv) (3-1 × 4-1) -1 × 5-1

(v) (4-1 – 5-1) ÷ 3-1

Express each of the following rational numbers with a negative exponent:

(i) (1/4)3

(ii) 35

(iii) (3/5)4

(iv) ((3/2)4)-3

(v) ((7/3)4)-3

Express each of the following rational numbers with a positive exponent:

(i) (3/4)-2

(ii) (5/4)-3

(iii) 43 × 4-9

(iv) ((4/3)-3)-4

(v) ((3/2)4)-2

Simplify:

(i) ((1/3)-3 – (1/2)-3) ÷ (1/4)-3

(ii) (32 – 22) × (2/3)-3

(iii) ((1/2)-1 × (-4)-1)-1

(iv) (((-1/4)2)-2)-1

(v) ((2/3)2)3 × (1/3)-4 × 3-1 × 6-1

By what number should 5-1 be multiplied so that the product may be equal to (-7)- 1?

By what number should (1/2)-1 be multiplied so that the product may be equal to (-4/7)-1?

By what number should (-15)-1 be divided so that the quotient may be equal to (- 5)-1?

By what number should (5/3)-2 be multiplied so that the product may be (7/3)-1?

Find x, if

(i) (1/4)-4 × (1/4)-8 = (1/4)-4x

(ii) (-1/2)-19 ÷ (-1/2)8 = (-1/2)-2x+1

(iii) (3/2)-3 × (3/2)5 = (3/2)2x+1

(iv) (2/5)-3 × (2/5)15 = (2/5)2+3x

(v) (5/4)-x ÷ (5/4)-4 = (5/4)5

(vi) (8/3)2x+1 × (8/3)5 = (8/3) x+2

(i) If x= (3/2)2 × (2/3)-4 , find the value of x-2.
(ii) If x = (4/5)-2 ÷ (1/4)2 , find the value of x-1.

Find the value of x for which 52x ÷ 5-3 = 55

Questions in Powers Exercise 2.3

Express the following numbers in standard form:

(i) 6020000000000000

(ii) 0.00000000000942

(iii) 0.00000000085

(iv) $^{846\times10^7}$

(v) $3759\times10^{-4}$

(vi) 0.00072984

(vii) $0.000437\times10^4$

(viii) 4 ÷ 100000

Write the following numbers in the usual form:

(i) $4.83\times10^7$

(ii) $3.02\times10^{-6}$

(iii) $4.5\times10^4$

(iv) $3\times10^{-8}$

(v) $1.0001\times10^9$

(vi) 5.8 × $10^2$

(vii) 3.61492 × $10^6$

(vii) 3.25 × $10^{-7}$

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Chapters in this book

Rational Numbers

Powers

Squares and Square Roots

Cube and Cube Roots

Playing with Numbers

Algebraic Expressions and Identities

Factorization

Division of Algebraic Expressions

Linear Equation in One Variable

Direct and Inverse Variations

Time and Work

Percentage

Profit Loss Discount and Value Added Tax

Compound Interest

Understanding Shapes Polygons

Understanding Shapes Quadrilaterals

Understanding Shapes Special Types Quadrilaterals

Practical Goemetry

Visualising Shapes

Area of Trapezium and Polygon

Volume Surface Area Cuboid Cube

Surface Area and Volume of Right Circular Cylinder

Classification And Tabulation Of Data

Classification And Tabulation Of Data Graphical Representation Of Data As Histograms

Pictorial Representation Of Data As Pie Charts Or Circle Graphs

Data Handling Probability

Introduction To Graphs