# How do you find the value of c and x that makes the equation c^(x+7)/c^(x-4)=c^11 true?

Jan 12, 2017

The equation is true $\forall x$ and any $c$

#### Explanation:

${c}^{x + 7} / {c}^{x + 4} = \frac{{c}^{x} \times {c}^{7}}{{c}^{x} \times {c}^{- 4}}$

$= \frac{\cancel{{c}^{x}} \times {c}^{7}}{\cancel{{c}^{x}} \times {c}^{- 4}}$

$= {c}^{7 + 4} = {c}^{11}$

Hence the expression $= {c}^{11}$ independent of $x$

Thus, the equation is true $\forall x$ and any $c$