Which expression is equivalent to

28p^9 q^-5/12p^-6 q^7

7p^15 / q^12

Step-by-step explanation:

7p^9+6 q^-5-7 / 3 #28 is divided by 12

7p^15 / q^12 #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