Answer:
7p^15/3q^12 is equivalent to 28p^9 q^-5/12p^-6 q^7
Step-by-step explanation:
Given Parameter:
28p^9 q^-5/12p^-6 q^7
Required; To simplify.
To simplify the above expression, we'll apply 2nd law of indices.
But first, let's rewrite the expression.
28p^9 q^-5/12p^-6 q^7 becomes
(28 * p^9 * q^-5) / (12 * p^-6 * q^7)
Then we collect similar indices. This is done as follows
(28/12) * (p^9/p^-6) * (q^-5/q^7)
From second law of indices (law of division);
If the two terms have the same base () and are to be divided their indices are subtracted.
For instance x^a/x^b = x^(a - b).
Applying this law; we have
(28/12) * (p^9/p^-6) * (q^-5/q^7) becomes
(28/12) * (p^(9 - (-6))) * (q^(-5-7))
(28/12) * (p^(9+6)) * (q^-12)
(28/12) * p^15 * q^-12
Simplify 28/12
(4*7)/(4*3) *p^15 * q^-12
(7/3) * p^15 * q^-12
(7/3) * p^15 * 1/q^12
7p^15/3q^12
Hence, 7p^15/3q^12 is equivalent to 28p^9 q^-5/12p^-6 q^7
