Question

State the product law of exponents.

Answer 1

The product law of exponents :  

When we multiply the two numbers with the same base we add the exponents of these rational numbers.

Let a (> 0) be a real number and p, q be rational numbers.  

a^p × a^q = a^p+q

Some examples :

(i) (4)⁴ × (4)³ = 4⁴⁺³ = 4⁷

(ii) (⅕)² × (⅕) = (⅕)²⁺¹ = (⅕)³

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Similar questions :

Simplify:

(i) (16⁻¹/⁵)⁵/² (ii) 3√(343)⁻² (iii) (0.001)¹/³ (iv) (25)³/² x(243)³/⁵ / (16)⁵/⁴ x (8)⁴/³

(v) (√2/5)⁸ ÷(√2/5)¹³ (vi) (5⁻¹x7²/5²x7⁻⁴)⁷/² x(5⁻²x7³/5³x7⁻5)⁻⁵/²

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Find:

(i) 64^(1/2)

(ii) 32^(1/5)

(iii) 125^(1/3)

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Answer 2

Answer:

Step-by-step explanation:

When we multiply the two numbers with the same base we add the exponents of these rational numbers.

Let a (> 0) be a real number and p, q be rational numbers.  

a^p × a^q = a^p+q