Solve (7×3)^y^x: Working with Nested Exponent Expressions

To solve this problem, let's simplify the expression $\left(\left(7\times3\right)^y\right)^x$ using the exponent rules. Here are the steps:

• Step 1: Identify the expression: $\left(\left(7\times3\right)^y\right)^x$.
• Step 2: Apply the power of a power rule for exponents: $(a^m)^n = a^{m \cdot n}$.
• Step 3: This rule states that when you raise an exponent to another power, you multiply the exponents. In this case, we have $\left(7\times3\right)^{y \cdot x}$.
• Step 4: The correct simplification is to combine the exponents: $(7\times3)^{yx}$.

After applying these steps, the simplified expression of $\left(\left(7\times3\right)^y\right)^x$ is $(7\times3)^{yx}$.

Comparing the given choices, choice 1: $(7\times3)^{yx}$ is consistent with the principle of exponents that was applied here.

Thus, the correct answer to the problem is $(7\times3)^{yx}$ as it's the only choice accurately representing the simplification according to exponent rules.