**Important questions for class 8 maths chapter 12 – exponents and powers,** with solutions are provided here by our subject experts. Practice these questions to score better marks in the exam as it covers the latest **CBSE syllabus (2020-2021)** and is as per **NCERT** book/curriculum.

The chapter exponents and powers will explain to represent very large numbers or very small numbers in a standard form. Students can reach us at Important Questions Class 8 Math to get important questions and solutions for all the chapters of Maths 8th Class.

**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

## Exponents And Powers Important Questions For Class 8 (Chapter 12)

Some important short answer type questions and long answer type questions from exponents and powers are given below.

### Short Answer Type Questions

**1. Find the value of (4 ^{0} + 4^{-1}) × 2^{2}**

**Solution: **

(4^{0} + 4^{ -1}) × 2^{2} = (1 + ¼) × 4

= 5/4 x 4

= 5

**2. Solve 3 ^{-4 }and (½)^{-2}**

**Solution:**

We know, b^{-n }= 1/b^{n}

So, 3^{-4 }= 1/3^{4 }= 1/81

And, (½)^{-2} = 1^{-2}/2^{-2} = 2^{2}/1^{2} = 4

**3. Simplify the following expression and express the result in positive power notation:**

**(−4) ^{5} ÷ (−4)^{8}**

**Solution: **

Using a^{m} ÷ a^{n} = a^{m-n}

(−4)^{5} ÷ (−4)^{8 }= (-4)^{5}/(-4)^{8}

⇒ (-4)^{5-8} = 1/ (-4)^{3}

**4. Evaluate a ^{2} × a^{3} × a^{-5}**

**Solution: **

a^{2} × a^{3} × a^{-5} = a^{2+3-5}

= a^{5-5}

= a^{0} = 1

**5. Express 4 ^{-3} as a power with base 2.**

**Solution:**

4^{-3 }can be written as:

4^{-3 }= (2^{2})^{-3}

Now, by using exponential law i.e. (a^{m})^{n} = a^{mn}

4^{-3} = 2^{-6} (which is in base 2 form).

### Long Answer Type Questions

**6. Evaluate (√4) ^{-3}**

**Solution:**

(√4)^{-3} = (4^{½})^{-3}

= 4^{-3/2} = 1/ 4^{3/2}

= 1/(4^{3})^{½} = 1/(64)^{½}

= 1/(8^{2})^{½} = 1/8

**7. Find the value of x for which 2 ^{x} ÷ 2^{-4} = 4^{5}**

**Solution:**

Given,

2^{x} ÷ 2^{-4} = 4^{5}

Now, 2^{x} × (½)^{-4} = (2^{2})^{5}

Or, 2^{x} × (½)^{-4} = 2^{10}

Thus, 2^{x+4 }= 2^{10}

⇒ x + 4 = 10

Hence, x + 4 = 10

So, x = 6

**8. Calculate the missing value of “x” in the following expression: (11/9) ^{3} × (9/11)^{6} = (11/9)^{2x-1}**

**Solution:**

Given: (11/9)^{3} × (9/11)^{6} = (11/9)^{2x-1}

The multiplier of L.H.S of the equation can be written as:

(11/9)^{3} × (11/9)^{-6} = (11/9)^{2x-1}

⇒ (11/9)^{3-6} = (11/9)^{2x-1}

Therefore, -3 = 2x – 1

2x = -3 + 1

x = -2/2

x = -1

**9. 5 books and 5 paper sheets are placed in a stack. Find the total thickness of the stack if each book has a thickness of 20 mm and each sheet has a thickness of 0.016 mm. **

**Solution:**

Given,

Thickness of 1 book = 20 mm

And,

Thickness of one paper = 0.016 mm

So, thickness of 5 books = 20 x 5 = 100 mm

And,

Thickness of 5 papers = 0.016 × 5 = 0.08 mm

Now, the total thickness of a stack is:

= 100 + 0.08 = 100.08 mm

= 100.08 10^{2} / 10^{2} mm

= 1.0008 × 10^{2 }mm

**10. If a new-born bear weighs 4 kg, calculate how many kilograms a five-year-old bear weigh if its weight increases by the power of 2 in 5 years?**

**Solution:**

Given,

Weight of new-born bear = 4 kg

Rate of weight increase in 5 years = power to 2

Thus, the weight of the 5-year old bear = 4^{2} = 16 kg

**Q.11: Simplify [25 x t ^{-4}]/[5^{-3} x 10 x t^{-8}]**

Solution:

We can write the given expression as;

[5^{2}x t

^{-4}]/[5

^{-3}x 5 x 2 x t

^{-8}]

= [5^{2} x t^{-4+8}]/[5^{-3+1} x2]

= [5^{2+2} x t^{4}]/[2]

= [5^{4} x t^{4}]/[2]

= [625/2] t^{4}

**Q.12: Express 0.00000000837 in standard form.**

Solution:

0.00000000837

= 0.00000000837 x 10^{9} / 10^{9}

= 8.37 ×10^{-9}

**Q.13: Write 3.61492 x 10 ^{6 }in usual form.**

Solution: 3.61492 x 10^{6}

= 3.61492 x 1000000

= 3614920

### Maths Class 8 Chapter 12 Extra Questions

- Evaluate: (-4)
^{-3} - Simplify: (𝟑
^{-7}÷ 𝟑^{-9}) × 𝟑^{-4} - Find the value of (3
^{7}+ 4^{-3}+ 5^{3})^{0} - Evaluate: [{1/2}
^{-1}+{1/3}^{-1}]^{-1} - Express 31860000000 in standard form.
- Find x so that (-5)
^{x+1}× (-5)^{5}= (-5)^{7} - Solve the following: (81)
^{-4}÷ (729)^{2-x}= 9^{4x}

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