Question

Plz solve this for me. 6.67× 10^-11 ×75 ×6× 10^24 / (6.4×10^6)^2 = 732.7

Answer 1

Hi there!
Here's the answer:

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Numerator of fraction
=> 6.67 × 10^(-11) × 75 × 6 × 10^(24)

• Multiply all numbers first except the number having power with base 10.

=> [ 6.67 × 75 × 6 ] × 10^(-11) × 10^(24)
=> 3001.5 × 10^(-11) × 10(24)

°•° (a^m) × (a^n) = a^(m+n)

=> 3001.5 × 10^(-11+24)
=> 3001.5 × 10^(13)
=> 30015 × 10^(-1) × 10^(13)
=> 30015 × 10^(12)


Denominator of fraction
=> (6.4×10^6)^2
=> (6.4)² × (10^6)^2

°•° (a^m)^n = a^(m×n)

=>40.96 × 10^(12)
=> 4096 × 10^(-2) × 10^(12)

°•° (a^m) × (a^n) = a^(m+n)

=> 4096 × 10^(-2+12)
=> 4096 × 10^(10)

Fraction
= [(30015 × 10^(12)) / (4096 × 10^(10)) ]
=> [(30015/4096)] × [10^(13)/10^(10)]

°•° a^m/a^n = a^(m-n)

=> 7.3278 × 10^(12-10)
=> 7.3278 × 10^ (2)
=> 732.7

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Hope it helps