Question

Simplify & evaluate :
[(10²) ⁴ x (5³)⁴]× (10^5)³×(2⁴)³]÷[(5⁴)² (10²)^5]×[(2²)⁴×(2²)²]​

Answer 1

Given:-

$\text{x}=\frac{[(10^2)^4\times(5^{3})^4)]\times(10^{5})^3\times(2^{4})^{3}]}{[(5^{4})^{2}\times(10^{2})^{5}]\times[(2^{2})^{4}\times(2^{2})^{2}]}$

To Find:-

Value of x.

Solution:-

$\frac{10^{8}\times5^{12}\times10^{15}\times2^{12}}{5^{8}\times10^{10}\times2^{8}\times2^{4}}$

Simplify the above equation.

$\frac{10^{23}\times5^{12}\times2^{12}}{10^{10}\times2^{12}\times5^{8}}$

$10^{13}\times5^{4}$

$(2\times5)^{13}\times5^{4}$

$2^{13}\times5^{13}\times5^{4}\\2^{13}\times5^{17}$

Answer 2

Given : [(10²) ⁴ x (5³)⁴]× (10^5)³×(2⁴)³]÷[(5⁴)² (10²)^5]×[(2²)⁴×(2²)²]​

To Find : Simplify & evaluate :

Solution:

[(10²) ⁴ x (5³)⁴]× (10⁵)³×(2⁴)³]÷[(5⁴)² (10²)⁵]×[(2²)⁴×(2²)²]​

 

[(10²) ⁴ x (5³)⁴]× (10⁵)³×(2⁴)³]

(10²) ⁴  = 10⁸  = (5 x 2)⁸ = 5⁸ x 2⁸

(5³)⁴ = 5¹²

(10⁵)³ = 10¹⁵ = (5 x 2)¹⁵ = 5¹⁵ x 2¹⁵

(2⁴)³ = 2¹²

Hence numerator becomes

5⁸ x 2⁸ x 5¹² x 5¹⁵ x 2¹⁵ x 2¹²

= 5³⁵ x 2³⁵

[(5⁴)² (10²)⁵]×[(2²)⁴×(2²)²]​

(5⁴)² = 5⁸

(10²)⁵  = 10¹⁰  = (5 x 2)¹⁰ = 5¹⁰ x 2¹⁰

(2²)⁴ = 2⁸

(2²)² = 2⁴

Hence denominator becomes

5⁸ x 5¹⁰ x 2¹⁰ x 2⁸ x 2⁴

= 5¹⁸ x 2²²

(5³⁵ x 2³⁵ ) ÷ (5¹⁸ x 2²²)

= 5¹⁷ x 2¹³

[(10²) ⁴ x (5³)⁴]× (10^5)³×(2⁴)³]÷[(5⁴)² (10²)^5]×[(2²)⁴×(2²)²]​  = 5¹⁷ x 2¹³

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