Find the missing factor or exponent(s).
-$$( x ? y ? ) ^ { 6 } = x ^ { 60 } y ^{72}$$
A) 54,66
B) 6,12
C) 10,12
D) 10,6

Question

Quizplus · Accepted Answer

To obtain the missing factor or exponent(s), we need to solve for them using the given equation.

First, we can simplify the left side of the equation by using the property of exponents that states: $(a^b)^c = a^{bc}$ for any nonzero real number $a$ and integers $b$ and $c$.

Thus, we have: 
$$(x^ay^b)^6 = x^{6a}y^{6b}$$

Comparing this with the right side of the given equation, we see that we must have:

$$6a = 60 \quad 	ext{and} \quad 6b = 72$$

Solving for $a$ and $b$, we get $a = 10$ and $b = 12$.

Therefore, the missing factor or exponent(s) are $10$ and $12$.

Choice C has these numbers, so it is the best choice.

Find the Missing Factor or Exponent(s) (x?y?)6=x60y72( x ? y ? ) ^ { 6 } = x ^ { 60 } y ^{72}(x?y?)6=x60y72

Find the Missing Factor or Exponent(s) $( x ? y ? ) ^ { 6 } = x ^ { 60 } y ^{72}$