## KrystaRenee What is the simplified form of this expression? (t^4/10y^4)^-4 10t^16y^16 10000y^16/t^16 -40t^16/t^16 10000t^16/10y one year ago one year ago

1. goformit100

2. KrystaRenee

Noo.

3. goformit100

I think its -40t^16/t^16

4. KrystaRenee

Can you explain why so I understand.

5. goformit100

because the given equation looks to be of the form Quadratic, i suppose...

6. jim_thompson5910

(t^4/10y^4)^-4 (10y^4/y^4)^4 [ (10y^4)^4 ]/[(y^4)^4] I'll let you finish up

7. KrystaRenee

I'm not sure what to do.

8. whpalmer4

$(\frac{t^4}{10y^4})^{-4} = \frac{1}{(\frac{t^4}{10y^4})^{4}}$ because $a^{-n} = \frac{1}{a^n}$ Now we can invert the fraction and make it be the numerator because dividing by a fraction is the same as multiplying by the reciprocal, and we're just multiplying it with 1. $(\frac{10y^4}{t^4})^4$Next, we use the properties of logs that $(a^n)^m = a^{n*m}$ and $(ab)^n = a^nb^n$$\frac{10^4y^{16}}{t^{16}}$

9. KrystaRenee

So the second option?

10. whpalmer4

What is the value of $$10^4$$?

11. KrystaRenee

10000.

12. whpalmer4

Okay, so you should be able to match the expression exactly against one of the answer choices with confidence.

13. KrystaRenee

Well then I'm confidently saying the second option lol.

14. whpalmer4

good. that's correct.