Solve for X: (2×7×21)/(5×6) Raised to Power X

To solve this problem, we'll follow these steps:

• Step 1: Understand the expression and the exponent rules.
• Step 2: Apply the exponent to both the numerator and denominator.
• Step 3: Simplify each part of the expression by distributing the exponent correctly.

Now, let's work through each step:
Step 1: The original expression is $\left(\frac{2\times7\times21}{5\times6}\right)^x$. It needs to be rewritten by applying the exponent to each part of the fraction according to the rules of exponents.
Step 2: Using $\left(\frac{a}{b}\right)^x = \frac{a^x}{b^x}$, we apply the exponent $x$ to both the numerator and denominator:
$\left(\frac{2\times7\times21}{5\times6}\right)^x = \frac{(2\times7\times21)^x}{(5\times6)^x}$
Step 3: Distribute the exponent $x$ across each multiplication in the numerator and the denominator according to the rule $(a \times b)^x = a^x \times b^x$:
In the numerator: $(2 \times 7 \times 21)^x = 2^x \times 7^x \times 21^x$.
In the denominator: $(5 \times 6)^x = 5^x \times 6^x$.
Thus, the expression becomes:
$\frac{2^x \times 7^x \times 21^x}{5^x \times 6^x}$

Therefore, the solution to the problem is $\frac{2^x\times7^x\times21^x}{5^x\times6^x}$.