Find the values of $c$ and $d$ that satisfy the equation $7 \times 10^c + 7 \times 10^d = 70700$.

1. Problem Description

Find the values of $c$ and $d$ that satisfy the equation $7 \times 10^c + 7 \times 10^d = 70700$.

2. Solution Steps

We are given the equation $7 \times 10^c + 7 \times 10^d = 70700$.

We can divide both sides of the equation by 7:

$\frac{7 \times 10^c + 7 \times 10^d}{7} = \frac{70700}{7}$

$10^c + 10^d = 10100$

We can rewrite $10100$ as $10000 + 100$, which are powers of 10:

$10100 = 10^4 + 10^2$

Therefore, $10^c + 10^d = 10^4 + 10^2$.

We can conclude that $c$ and $d$ are 4 and 2, respectively. Since the order does not matter, we can have $c=4$ and $d=2$, or $c=2$ and $d=4$.

3. Final Answer

$c = 4, d = 2$ or $c = 2, d = 4$