Question

evaluate using suitable laws of exponent 16×10²×64/2⁴×4²​

Answer 1

Answer:

The value of 16×10²×64/2⁴×4²​ is 102400.

Step-by-step explanation:

• In the context to the given question, we have to evaluate value of the given problem

⇒ GIVEN:

16×10²×64/2⁴×4²​

⇒ SOLUTION:

Laws of exponents

xᵃ xᵇ= xᵃ⁺ᵇ

xᵃ/xᵇ = x ᵃ⁻ᵇ

(xᵃ)ᵇ = xᵃᵇ

[ base should be same for any of the operation]

16×10²×64/2⁴×4²​

Now by transforming our problem into same base to solve it easily;

we know that,

16 = 2 x2x2x2 = (2)⁴

64 = 2x2x2x2x2x2 = (2)⁶

4 = 2 x2 = (2)²

now by replacing this, we get,

(2)⁴ x 10² x [(2)⁶/(2)⁴] x (2²)²

now by applying the above mention laws;

we get

⇒ 2⁴ x 10² x (2)⁶⁻⁴ x 2²ˣ²

⇒ 2⁴ x 10² x 2² x 2⁴

⇒ 2 ⁴⁺²⁺⁴ x 10²          [xᵃ xᵇ= xᵃ⁺ᵇ ]

⇒ 2¹⁰ x 10²        

⇒ 1024 x 100

⇒ 102400

Therefore, The value of 16×10²×64/2⁴×4²​ is 102400.