Solve (3×7)/(5×8) Raised to Power -3: Negative Exponent Challenge

To simplify the expression $\left(\frac{3\times7}{5\times8}\right)^{-3}$, we follow these steps:

• Step 1: Apply the rule for negative exponents, which states that $a^{-b} = \frac{1}{a^b}$. For fractions, $\left(\frac{a}{b}\right)^{-n} = \frac{b^n}{a^n}$.
• Step 2: Rewrite the expression by applying this rule:
  $\left(\frac{3\times7}{5\times8}\right)^{-3} = \frac{(5\times8)^3}{(3\times7)^3}$
• Step 3: Simplify the expression by recognizing the bases to the power of 3: $\frac{(5\times8)^3}{(3\times7)^3}$

The expression can be left as is because it matches one of the choices provided. Performing further calculations here is unnecessary since we have correctly applied the negative exponent rule.

Therefore, the correct simplified form of the expression is $\frac{(5\times8)^3}{(3\times7)^3}$, which corresponds to choice 2.