simplify 3^-5 * 10^-5 * 125/6^-5 * 5^-7 answer asap pleaase
Answers
Answer:
The answer is (5)^-27
Step-by-step explanation:
To simplify
Step 1 = First make the powers of all the numbers positive
That is,
= (1/3)^5 X (1/10)^5 X (6/125)^5 X (1/5)^7
We know that if powers are same of the numbers in the multiplication
then we multiply the base with each other by keeping the power common
That is,
= (1/3 X 1/10 X 6/125)^5 X (1/5)^7
After multiplying
= (1/5 X 1/125)^5 X (1/5)^7
= (1/625)^5 X (1/5)^7
Step 2 = Make the base same, so that we can add the powers[according to the rule]
First of all make powers negative again, so that we can easily simplify
That is,
= (625)^-5 X (5)^-7
Then,
we know that 625 = (5)^4
So,
= [(5)^4]^-5 X (5)^-7
= (5)^4 X -5(POWERS GOT MULTIPLIED)] X (5)^-7
= (5)^-20 X (5)^-7
We know that when the bases are same of the numbers in multiplication we add the powers
That is,
= (5)^-20 +[-7]
= (5)^-27