# Evaluate

(i) (8^{−1}× 5^{3})/2^{−4 }(ii) (5^{−1}× 2^{−1})×6^{−1}

**Solution:**

(i) (8^{−1 }× 5^{3}) / 2^{−4}

According to the rules of exponents,

We know that, a^{−m }= 1/a^{m},a^{m}÷a^{n }= a^{m−n}

(8^{−1}× 5^{3})/2^{−4}

= (2^{4 }× 5^{3})/8^{1} [Since a^{−m }= 1/a^{m}]

= (2^{4 }× 5^{3})/2^{3 }

= 2^{4 − 3 }× 5^{3} [a^{m }÷ a^{n }= a^{m − n}]

= 2 × 125

= 250

(ii) (5^{−1}× 2^{−1}) × 6^{−1}

According to the rules of exponents,

We know that, a^{m }× b^{m }= (ab)^{m}, a^{-m} = 1/a^{m}

(5^{−1 }× 2^{−1}) × 6^{−1 }

=10^{−1}× 6^{−1}

= (10 × 6)^{−1 }[∵a^{m }× b^{m }= (ab)^{m}]

= (60)^{−1 }= 1/60 [∵ a^{-m} = 1/a^{m}]

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 12

**Video Solution:**

## Evaluate (i) (8⁻¹ × 5³)/2⁻⁴^{ }(ii) (5⁻¹ × 2⁻¹) × 6⁻¹

Class 8 Maths NCERT Solutions Chapter 12 Exercise 12.1 Question 4

**Summary:**

The value of the following expressions are: (i) (8^{−1}× 5^{3})/2^{-4} = 250 (ii) (5^{−1 }× 2^{−1}) × 6^{−1} = 1/60

**☛ Related Questions:**

- Evaluate (i) 3-2 (ii) (4)-2 (iii) (1/2)-5.
- Simplify and express the result in power notation with positive exponent. (i) (−4) 5 ÷ (−4) 8 (ii) (1 / 23) 2 (iii) (−3) 4 × (5/3) 4 (iv) (3 -7 ÷ 3 -10) × 3 -5 (v) 2 -3 × (−7) -3
- Find the value of (i) (30 × 4−1) × 22 (ii) (2−1 × 4−1) ÷ 2−2 (iii) (1/2)−2 + (1/3)−2 + (1/4)−2 (iv) (3−1 +4−1 + 5−1)0 (v) {(−2/3)−2}2
- Find the value of m for which (5m ÷ 5−3) = 55

visual curriculum