1.

Simplify 3^-5 * 10^-5 * 125/6^-5 * 5^-7 answer asap pleaase

Answer»

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


Discussion

No Comment Found

Related InterviewSolutions