Question

Find the product. (0.5n^5)^2(10n^7)^3

Answer 1

Step-by-step explanation:

$(0.5 {n}^{5} )^{2} (10 {n}^{7} )^{3} \\ = (0.5)^{2} {n}^{5 \times 2} \times {10}^{3} {n}^{7 \times 3} \\ = 0.25 {n}^{10} \times 1000 {n}^{21} \\ = (0.25 \times 1000){n}^{21 + 10} \\ \purple{ \boxed{ \bold{ (0.5 {n}^{5} )^{2} (10 {n}^{7} )^{3} = 250{n}^{31}}}}$

Answer 2

Answer:

250^31 is the correct answer

Step-by-step explanation:

I don't know why the person's answer before me is marked incorrect.  It's the correct answer.  

If you find out what the first set of parentheses is you'll get

.25n^10

You get that by finding .5n x .5n and you get .25n

You get 10 as your exponent by multiplying the outer exponent (which is 2)

by 5.

If you find out what the second set of parentheses are you will get 1,000n^21

You get this by figuring out what 10 to the third power is, you'll get 1,000

Then you multiply the exponents and get 21, given that your exponents are 7 and 3.

Then you combine .25n^10 and 1000n^21 and get 250^31

You know this because 1000 x .25 is 250.

Then you add your exponents and get 31

You combine everything and get 250n^31

Hope I helped!!!

Have a great day:)