Class 8 Maths

# Exponents and Power

## Exercise 12.1

Question 1: Evaluate.

(i) 3^{–2}

(ii) (– 4)^{– 2}

Answer: = 2²+3²+4² = 4+9+16 = 29

Question 2: Simplify and express the result in power notation with positive exponent.

**Alternate Method:**

= -3^{4} x 5^{4} ÷3^{4} (the power on 3 is even so -3^{4} = 3^{4})

=3^{0} x 5^{4}=625

(iv) (3^{–7} ÷Answer: Using a^{m}÷ a^{n} = a^{m-n}

(3^{–7} ÷ 3^{–10}) = 3^{-7+10} = 3^{3}

Hence, (3^{–7} ÷ 3^{–10}) × 3^{–5}

=3^{3} x 3–5

Now, a^{m} x a^{n }= a^{m+n}

Hence, = 3^{3} x 3^{–5}

= 3^{3-5 }= 3^{-2}

(v) 2^{– 3} × (–7)^{–3}

**Answer:** 2^{– 3} × (–7)^{–3}

Question 3: Find the value of.

(i) (3° + 4^{–1}) × 2^{2}

**Answer:** (3° + 4^{–1}) × 2^{2}

(ii) (2–1 × 4–1) ÷ 2–2

(iii) (3^{–1} + 4^{–1} + 5^{–1})^{0}

**Answer:** aº=1

Hence, (3^{–1} + 4^{–1} + 5^{–1})^{0} = 1

Question 4: Evaluate

(ii) (5^{–1} × 2^{–1}) × 6^{–1}

Question 5: Find the value of m for which 5^{m} ÷ 5^{–3} = 5^{5}

**Answer:** a^{m} = a^{m-n}

Here, m-n = 5 and n = -3

So, m = 5+(-3)=2

Question 6: Evaluate

**Answer:** (3-4)-1 = (-1)-1 =-1

Question 7: Simplify.

(i) (25 x t^{-4}) ÷ (5^{-3} x 10 x t^{-8})

**Answer:** (25 x t^{-4}) ÷ (5^{-3} x 10 x t^{-8})

=(5² x t^{-4}) ÷ (5^{-3} x 5 x 2 x t^{-8})

= 5^{2+2} x t^{-4+8} ÷ 2

= 5^{4} x t^{4} ÷ 2

(ii) (3^{-5} x 10^{-5} x 125) ÷ (5^{-7} x 6^{-5})

**Answer:**

= (3^{-5} x 5^{-5} x 2^{-5} x 5^{3}) ÷ (5^{-7} x 6^{-5})

= (3^{-5} x 5^{-5+3} x 2^{-5}) ÷ (5^{-7} x 6^{-5})

= (3^{-5} x 5^{-2} x 2^{-5}) ÷ (5^{-7} x 3^{-5} x 2^{-5})

= (3^{-5+5} x 5^{-2+7} x 2^{-5+5})

= (3^{0} x 5^{5} x 2^{0})

=3125