Simplify: (35 × 105 × 25)/ (57 × 65 )Simplify: (35 × 105 × 25)/ (57 × 65 )

Dear Student105 can be written as = (5 × 2)5= 55 × 2525 can be written as = 5 × 5= 5265 can be written as = (2 × 3)5= 25 × 35Then we have,= (35 × 55 × 25 × 52)/ (57 × 25× 35)= (35 × 55+2× 25)/ (57 × 25 × 35) ... [∵am × an = am + n]= (35 × 57 × 25)/ (57 × 25 × 35)= (35-5 × 57 – 7 × 25-5) = (30 × 50 × 20) ... [∵am ÷ an = am – n]= 1 × 1× 1= 1Thanks

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Grade 12th passAlgebra

Simplify:
(3⁵ × 10⁵ × 25)/ (5⁷ × 6⁵ )
Simplify:
(3⁵ × 10⁵ × 25)/ (5⁷ × 6⁵ )

Harshit Singh

5 Years agoGrade 12th pass

1 Answer

Harshit Singh

5 Years ago

Dear Student

10⁵ can be written as = (5 × 2)⁵
= 5⁵ × 2⁵
25 can be written as = 5 × 5
= 5²
6⁵ can be written as = (2 × 3)⁵
= 2⁵ × 3⁵
Then we have,
= (3⁵ × 5⁵ × 2⁵ × 5²)/ (5⁷ × 2⁵× 3⁵)
= (3⁵ × 5⁵⁺²× 2⁵)/ (5⁷ × 2⁵ × 3⁵) ... [∵a^m × aⁿ = a^{m + n}]
= (3⁵ × 5⁷ × 2⁵)/ (5⁷ × 2⁵ × 3⁵)
= (3^5-5 × 5^{7 – 7} × 2^5-5)
= (3⁰ × 5⁰ × 2⁰) ... [∵a^m ÷ aⁿ = a^{m – n}]
= 1 × 1× 1
= 1

Thanks