Question

simplify
3^-5 × 10^-5 × 5³ × 7²/ 5^-7 × 2^-5 × 3^-5 × 7³ × 5²​

Answer 1

Answer:

5^3/7

Step-by-step explanation:

3^-5 × 10^-5 × 5³ × 7²/ 5^-7 × 2^-5 × 3^-5 × 7³ × 5²​

First, cancel out the 3^-5 from both denominator and numerator

So it becomes;

10^-5 × 5³ × 7²/ 5^-7 × 2^-5 × 7³ × 5²​

Now, expand 10^-5 as 2^-5 x 5^-5 (a^m x b^m = (ab)^m)

Then cancel the 2^-5 from denominator and numerator.

So it will be like this;

5^-5 × 5³ × 7²/ 5^-7 × 7³ × 5²​

Now, take the 7^3 to the top, so it becomes 7^-3

And add it to 7^2

Therefore we have 7^-1 in numerator. Take that to denominator because a^-m = 1/a^m

So now we have

5^-5 × 5³ / 5^-7 × 7 × 5²​

Now for the 5^x terms. Take 5^-7 and 5^2 to the numerator. Remeber to change their exponent's sign when you do. So it becomes

5^-5 x5^3 x 5^7 x 5^-2 / 7

Therefore after adding all the terms it becomes 5 raised to (-5 + 3+ -2 + 7)

Therefore 5^3/7.

Hope this helped! Please let me know if I made a mistake in calculating.