## Exponents and Powers Class 8 Extra Questions Maths Chapter 12

**Extra Questions for Class 8 Maths Chapter 12 Exponents and Powers**

### Exponents and Powers Class 8 Extra Questions Very Short Answer Type

Question 1.

Find the multiplicative inverse of:

(i) 3^{-3}

(ii) 10^{-10}

Solution:

Question 2.

Expand the following using exponents.

(i) 0.0523

(ii) 32.005

Solution:

Question 3.

Simplify and write in exponential form.

Solution:

Question 4.

Simplify the following and write in exponential form.

Solution:

Question 5.

Express 8^{-4} as a power with the base 2.

Solution:

We have 8 = 2 × 2 × 2 = 2^{3}

8^{-4} = (2^{3})^{-4} = 2^{3×(-4)} = 2^{-12}

Question 6.

Simplify the following and write in exponential form.

(i) (3^{6} ÷ 3^{8})^{4} × 3^{-4}

(ii) \(\frac { 1 }{ 27 }\) × 3^{-3}

Solution:

Question 7.

Find the value of k if (-2)^{k+1} × (-2)^{3} = (-2)^{7}

Solution:

(-2)^{k+1} × (-2)^{3} = (-2)^{7}

⇒ (-2)^{k+1+3} = (-2)^{7}

⇒ (-2)^{k+4} = (-2)^{7}

⇒ k + 4 = 7

⇒ k = 3

Hence, k = 3.

Question 8.

Simplify the following:

Solution:

Question 9.

Find the value of \(\left[ \left( -\frac { 3 }{ 4 } \right) ^{ -2 } \right] ^{ 2 }\)

Solution:

Question 10.

Write the following in standard form

(i) 0 0035

(ii) 365.05

Solution:

### Exponents and Powers Class 8 Extra Questions Short Answer Type

Question 11.

Find the value of P if

Solution:

Question 12.

Solution:

Question 13.

Find the value of x if

Solution:

⇒ 3 + x = 18 [Equating the powers of same base]

x = 18 – 3 = 15

Question 14.

Solve the following: (81)^{-4} ÷ (729)^{2-x} = 9^{4x}

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Find x so that (-5)^{x+1} × (-5)^{5} = (-5)^{7} (NCERT Exemplar)

Solution:

(-5)^{x+1} × (-5)^{5} = (-5)^{7}

(-5)^{x+1+5} = (-5)^{7} {a^{m} × a^{n} = a^{m+n}}

(-5)^{x+6} = (-5)^{7}

On both sides, powers have the same base, so their exponents must be equal.

Therefore, x + 6 = 7

x = 7 – 6 = 1

x = 1.