Question

Which expression is equivalent to

Answer 1

The correct answer option is
`\frac {7 p^(15)} {3q^(12)}`.

Explanation:

We are given the following expression and we are to figure out which of the given answer options is equivalent to this expression:

`\frac {28 p^9 q^(-5) } {12 p^(-6) q^7}`

Cancelling the numbers by their greatest common factor and eliminating the negative exponents by moving them from numerator to denominator or from denominator to numerator.

`(7p^(15))/(3q^(12))`

Answer 2

For this case, we must find an expression equivalent to:

`\frac {28p ^ 9 * q ^ {- 5}} {12p ^ {- 6} * q ^ 7}`

By definition of power properties we have:

`a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}`

Rewriting the previous expression we have:

We take into account that:

`\frac {28} {12} = \frac {14} {6} = \frac {7} {3}`

So:

`\frac {7p ^ 9 * p ^ 6} {3q ^ 5 q ^ 7} =`

According to one of the properties of powers of the same base, we must put the same base and add the exponents:

`\frac {7p ^ {9+6}} {3q ^ {5+7}} =\\\frac {7p ^ {15}} {3q ^ {12}}`

Answer:

`\frac {7p ^ {15}} {3q ^ {12}}`

Option B