Solve (7×13)/(6×10×12) Raised to -3 Power: Complex Fraction Challenge

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

• Step 1: Identify the original fraction inside the expression, which is $\frac{7 \times 13}{6 \times 10 \times 12}$.
• Step 2: Apply the negative exponent rule, which states $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^{n}$. This means we need to find the reciprocal of the fraction and change the sign of the exponent to positive.

Now, let's work through these steps:

Step 1: The problem gives us the expression $\left(\frac{7 \times 13}{6 \times 10 \times 12}\right)^{-3}$.

Step 2: Using the reciprocal rule for negative exponents, we will rewrite the given expression by taking the reciprocal of the fraction:
$\left(\frac{7 \times 13}{6 \times 10 \times 12}\right)^{-3} = \left(\frac{6 \times 10 \times 12}{7 \times 13}\right)^{3}$

By applying the rule, the expression becomes $\left(\frac{6 \times 10 \times 12}{7 \times 13}\right)^3$, which is the required positive exponent form.

Therefore, the correct expression corresponding to the problem is $\left(\frac{6 \times 10 \times 12}{7 \times 13}\right)^3$.