Simplify: (25 × 52 × t8 )/ (103 × t4)Simplify: (25 × 52 × t8 )/ (103 × t4)

Dear Student

25 can be written as = 5 × 5
= 5²
10³ can be written as = 10³
= (5 × 2)³
= 5³ × 2³
We have,
= (5² × 5² × t⁸)/ (5³ × 2³ × t⁴)
= (5^{2 + 2} × t⁸)/ (5³ × 2³ × t⁴) ... [∵a^m × aⁿ = a^{m + n}]
= (5⁴ × t⁸)/ (5³ × 2³ × t⁴)
= (5^{4 – 3} × t^{8 – 4})/ 2³ ... [∵a^m ÷ aⁿ= a^{m – n}]
= (5 × t⁴)/ (2 × 2 × 2)
= (5 t⁴)/ 8

Thanks