Question

((5pq^3) / (4p^3q))^2

Answer 1

Here is the actual equation: \[(\frac{ 5pq^3 }{ 4p^3q })^2\]

Answer 2

Do you know the law of indices?

Answer 3

no

Answer 4

These are the law of indices, the rules for algebraic manipulation of indices:
\[x^a x^b = x^{a+b}\]\[(x^a)^b=(x^b)^a=x^{ab}\]\[x^{-a}=\frac{1}{x^a}\]

Answer 5

\[(x^a y^b)^c=x^{ac}y^{bc}\]

Answer 6

So if we apply these rules into the equation:
\[(\frac{5pq^3}{4p^3q})^2=\frac{(5pq^3)^2}{(4p^3q)^2}=\frac{5^2p^2(q^3)^2}{4^2(p^3)^2q^2}\]

Answer 7

\[=\frac{25p^2 q^6}{16p^6 q^2}=\frac{25}{16}p^2q^6(p^6q^2)^{-1}=\frac{25}{16}p^2p^{-6}q^6q^{-2}=\frac{25}{16}p^{2-6}q^{6-2}=\frac{25}{16}p^{-4}q^4=\frac{25q^4}{16p^4}\]

Answer 8

Wait so the answer comes out to \[\frac{ 25 }{ 16 }p ^{-4}\]

Answer 9

The answer is \[\frac{25}{16}p^{-4}q^4\]

Answer 10

oh ok thank you!

Answer 11

No probs