7^{8}=7^{8}\cdot7^x

The equation you've given is "7^8 = 7^8 * 7^x".

In this equation, we can see that both sides of the equation are equal.

The rule of exponents states that when you multiply two exponents with the same base, you add the powers. So, 7^8 * 7^x would be 7^(8+x).

Therefore, the equation becomes 7^8 = 7^(8+x).

Since the bases are the same (7), the exponents must also be equal.

So, 8 = 8 + x.

Subtract 8 from both sides to solve for x, and you get x = 0.

So, the solution to the equation "7^8 = 7^8 * 7^x" is x = 0.