Question

Which expression is equivalent to

Answer 1

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

Answer 2

Answer:

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

Step-by-step 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.

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