Which expressions are equivalent to the one below? Check all that apply. $\frac{25^{x}}{5^{x}}$ A. $(25-5)^{x}$ B. 5 C. $\frac{5^{x} \cdot 5^{x}}{5^{x}}$ D. $5^{x}$ E. $25^{x}$ F. $\left(\frac{25}{5}\right)^{x}$

Step 1 ：The given expression is \(\frac{25^{x}}{5^{x}}\). We know that 25 = 5^2, so we can rewrite the expression as \(\frac{(5^2)^{x}}{5^{x}}\). Using the power of a power rule, we can simplify this to \(\frac{5^{2x}}{5^{x}}\). Using the quotient of powers rule, we can simplify this further to \(5^{2x-x} = 5^{x}\). So, the given expression is equivalent to \(5^{x}\).

Step 2 ：Now, let's check each of the given options.

Step 3 ：A. \((25-5)^{x}\): This is equivalent to \(20^{x}\), which is not the same as \(5^{x}\).

Step 4 ：B. 5: This is a constant, not an expression involving x, so it's not equivalent to \(5^{x}\).

Step 5 ：C. \(\frac{5^{x} \cdot 5^{x}}{5^{x}}\): This simplifies to \(\frac{5^{2x}}{5^{x}} = 5^{x}\), so it is equivalent to the given expression.

Step 6 ：D. \(5^{x}\): This is exactly the same as the simplified form of the given expression, so it is equivalent.

Step 7 ：E. \(25^{x}\): This is not the same as \(5^{x}\), so it's not equivalent to the given expression.

Step 8 ：F. \(\left(\frac{25}{5}\right)^{x}\): This simplifies to \(5^{x}\), so it is equivalent to the given expression.

Step 9 ：So, the expressions equivalent to the given expression are C, D, and F.

Step 10 ：Final Answer: The expressions equivalent to the given expression are \(\boxed{C, D, F}\).