# Simplify and express the result in power notation with positive exponent

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

(iv) (3^{ -7 }÷ 3 ^{-10}) × 3^{ -5 }(v) 2^{ -3 }× (−7) ^{-3}

**Solution:**

The exponent of a number shows how many times the number is multiplied by itself.

(i) (−4)^{5 }÷ (−4)^{8}

According to the rules of exponents,

we know that a^{m}/a^{n }= a^{m − n} where m and n are integers.

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

(−4)^{−3 }

= 1/(−4)^{3}

(ii) (1/2^{3})^{2}

According to the rules of exponents,

we know that for any non-zero integer a, (a^{m})^{n }= a^{mn}

(1/2^{3})^{2 }

= 1/2^{6}

(iii) (−3)^{4} × (5/3)^{4}

According to the rules of exponents,

We know that a^{m }× b^{m }=(ab)^{m} and (a/b)^{m} = a^{m}/b^{m }where a & b are non-zero integers and m is an integer

(−3)^{4} × (5/3)^{4}

(−1 × 3)^{4 }× 5^{4}/3^{4 }

(−1)^{4 }× 5^{4 }

= 5^{4 }[∵(−1)^{4 }= 1]

(iv) (3^{−7 }÷ 3^{−10}) × 3^{−5}

According to the rules of exponents,

We know a^{m}/a^{n }= a^{m − n} and a^{m }× a^{n }= a^{m + n}

(3^{−7 }÷ 3^{−10}) × 3^{−5 }= (3^{−7−(−10)}) × 3^{−5}

= (3^{−7 + 10}) × 3^{−5 }= 3^{3 }× (3^{−5})

= 3^{3 + (−5)}

= 3^{−2 }= 1/3^{2}

(v) 2^{−3 }× (−7)^{−3}

According to the rules of exponents,

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

2^{−3 }× (−7)^{−3 }

= [2 × (−7)]^{−3 }

= (−14)^{−3}

= 1/(-14)^{3} [Since a^{−m }= 1/a^{m}]

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

**Video Solution:**

## 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

Class 8 Maths NCERT Solutions Chapter 12 Exercise 12.1 Question 2

**Summary:**

The following expressions are simplified and the result is expressed in power notation with a positive exponent. (i) (−4)^{ 5} ÷ (−4) 8 = 1/(−4)^{3} (ii) (1 / 2^{3})^{ 2 }= 1/2^{6}(iii) (−3)^{ 4} × (5/3)^{ 4 }= 5^{4 }(iv) (3^{ -7 }÷ 3 ^{-10}) × 3^{-5} = 1/3^{2} (v) 2^{ -3 }× (−7) ^{-3} = 1/(-14)^{3}

**☛ Related Questions:**

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