Exponents and powers class 8 questions are provided here with solutions and explanations, to help students understand the basic concepts of exponents and powers. These questions are designed as per the latest CBSE/ICSE curriculum guidelines for class 8. Practising these worksheets will clear their doubts and help them to solve higher-order thinking level questions asked in the examinations.

Also, Check

• Important 2 Marks Questions for CBSE 8th Maths
• Important 3 Marks Questions for CBSE 8th Maths
• Important 4 Marks Questions for CBSE 8th Maths

If x is added n times repeatedly, it simply implies n × x = nx, but if we multiply x, n times repeatedly it means xⁿ. Thus, xⁿ is an exponential form, any number written like this is called exponents. In xⁿ, x is called the base of the exponent and n is called the power

Learn more about exponents and powers.

Exponents and Powers Class 8 Questions with Solutions

Below are the practice questions on exponents and powers for class 8 with detailed solutions.

Question 1: Simplify (27)^2/3 – (81)^1/2.

Solution:

(27)^2/3 – (81)^1/2 = (3³)^2/3 – (9²)^1/2

= 3 ^{3 × ⅔} – 9 ^{2 × ½}

= 3² – 9

= 9 – 9 = 0

∴ (27)^2/3 – (81)^1/2 = 0.

Question 2: If 3^{x – y} = 27 and 3^{x + y} = 243, then what is the value of x and y?

Solution:

Given, 3^{x – y} = 27 = 3³ and 3^{x + y} = 243 = 3⁵

Comparing the powers on both sides of the exponents, we get

⇒ x – y = 3 ….(i)

x + y = 5 ….(ii)

Adding equations (i) and (ii),

2x = 8

⇒ x = 4

then y = 1.

Question 3: Simplify the following:

Solution:

Using the laws of exponents,

= -2⁶/(3⁹ × 5⁵).

Question 4: Determine (8x)^x if 9^{x + 2} = 240 + 9^x.

Solution:

We have,

9^{x + 2} = 240 + 9^x

⇒ 9^x. 9² – 9^x = 240

⇒ 9^x (9² – 1) = 240

⇒ 9^x × (81 – 1) = 240

⇒ 9^x = 240/80 = 3

⇒ (3²)^x = 3

Comparing powers on both the sides,

2x = 1 ⇒ x = ½

∴ (8x)^x = (8 × ½)^½ = 4^1/2 = 2.

Also Read:

• Ratio and Proportion
• Scientific Notation
• Algebraic Expressions
• Factorisation

Question 5: Simplify:

(i) 8x⁵y⁷/ 12x⁹y⁴

(ii) ( –5x³/2y ^–4)^–3

Solution:

(i)8x⁵y⁷/ 12x⁹y⁴ = ⅔ (x^{5 – 9} y^{7 – 4}) = 2y³/3x⁴.

(ii) ( –5x³/2y ^–4)^-3 = [( –5) ^{– 3} × (x³) ^{– 3}] / [2 ^–3. (y^–4) ^{– 3}]

= { –8 × x^–9}/{125 y¹²}

= –8/125x⁹y¹².

Question 6: Given, 10^0.48 = x and 10^0.70 = y and x^z = y², then find the approximate value of z.

Solution:

Given, x^z = y² ⇒ (10^0.48)^z = (10^0.70)²

⇒ 10 ^0.48z = 10^1.40 ⇒ 0.48z = 1.40

⇒ z = 140/48 = 2.9 (approx.)

Question 7: If 5^{3x + 2} = 25 × 5^{(4x – 1)}, then find the value of x.

Solution:

We have, 5^{3x + 2} = 25 × 5^{(4x – 1)}

⇒ 5^{3x + 2} = 5² × 5^{(4x – 1)}

⇒ 5^{3x + 2} = 5^{(2 + 4x – 1)}

⇒ 5^{3x + 2} = 5^{4x + 1}

As the bases are equal, comparing powers on both side we get,

3x + 2 = 4x + 1

⇒ 4x – 3x = 2 – 1

⇒ x = 1.

Question 8: If 5^x = 3^y = 45^z, then prove that 1/z = 1/x + 2/y.

Solution:

Given, 5^x = 3^y = 45^z

Then, 5^x = 45^z = (5 × 9)^z

⇒ 5^x = 5^z × (3²)^z

⇒ 5^x = 5^z × 3^2z …(i)

Similarly, 3^y = 5^z × 3^2z …(ii)

Multiplying equation (i) and (ii), we get,

5^x.3^y = (5^z × 3^2z)²

⇒ 5^x.3^y = 5^2z. 3^4z

Comparing powers on both sides.

x = 2z and y = 4z

⇒ 2/x = 1/z and 4/y = z

Adding both the equations,

2/z = 2/x + 4/y

⇒ 1/z = 1/x + 2/y.

Question 9: Simplify:

Solution:

Using the laws of exponents,

=162/4

= 40.5.

Question 10: Evaluate: (21² – 15²)^4/3

Solution:

(21² – 15²)^{4/3 .}= (441 – 225)^4/3 = (216)^4/3

= (∛216)⁴ = 6⁴ = 1296

Question 11: If (1331) ^{– x} = (225)^y, where x and y are integers, then find the value of 3xy.

Solution:

(1331) ^{– x} = (225)^y

⇒ (11³) ^–x = (15²)^y

⇒ 11^–3x = 15^2y

The above equation is true only for x = y = 0

∴ 3xy = 3 × 0 × 0 = 0.

Question 12: If (243) ^{– x} = (729)^y = 3³, then find the value of 5x + 6y.

Solution:

Now, (243) ^–x = 3³

⇒ (3^5.) ^–x = 3³

Comparing the powers,

–5x = 3 ⇒ x = –⅗

Again, (729)^y = 3^3.

⇒ (9³)^y = 3³

⇒ (3²)^3y = 3³

⇒ 3^6y = 3³

Comparing the powers,

6y = 3 ⇒ y = ½

∴ 5x + 6y = 5 × ( –3/5) + 6 × ½

= –3 + 3 = 0

Question 13: If 2 = 10^m and 3 = 10ⁿ, then find the value of 0.15.

Solution:

0.15 = 1.5/10 = 3/(2 × 10) [as 1.5 = 3/2]

= 10ⁿ/(10^m × 10)

= 10 ^{n – m – 1}

Question 14: Given, a = 2^x, b = 4^y, c = 8^z and ac = b². Find the relation between x, y and z.

Solution:

Given, ac = b²

⇒ 2^x. 8^z = (4^y)²

⇒ 2^x . 2^3z = 2^4y

⇒ 2^{x + 3z} = 2^4y

Comparing the powers on both sides,

x + 3z = 4y.

Question 15: Find the value of [169 ^–3/ 196 ^{– 8}]^1/48.

Solution:

[169 ^–3/ 196 ^{– 8}]^1/48 = [(13²) ^–3/ (14²) ^{– 8}]^1/48

= [13 ^{–3 × 2}/ 14 ^{– 8 × 2}]^1/48

= [13 ^–6/ 14 ^{– 16}]^1/48

= [14 ¹⁶/ 13 ⁶]^1/48

= (14) ^{16 × 1/48} / 13 ^{6 × 1/48}

= 14^1/3 / 13 ^⅛.

Practice Worksheet

1. Simplify:

(i) [3⁶ ÷ 3⁴]³

(ii) [(–2)⁵ × (3)⁵]² ÷ [12 × 3⁷]

(iii) [(2³ × 3⁴)³ × (–5)³] ÷ [60 × (–2)⁵]

2. If (1331) ^{– x} = (225)^y, where x and y are integers, then find the value of 3 + xy.

3. If (243) ^{– x} = (729)^y = 27, then find the value of 5x – 6y.

4. (4)^½ × (0.5)⁴ is equal to _______.

5. If 2^x = 4^y = 8^z and xyz = 288, then prove that 1/2x + 1/4y + 1/8z = 11/96.