Evaluate (6×8)/(2×7) Raised to the Power of -5: Complex Fraction Exercise

To solve the problem, we need to find the equivalent expression for the given negative exponent:

Step 1: Identify the base fraction as $\frac{6\times8}{2\times7}$.

Step 2: Apply the negative exponent rule:

The expression $\left(\frac{6\times8}{2\times7}\right)^{-5}$ can be rewritten using the property that $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$.

Thus, we have:

$\left(\frac{6\times8}{2\times7}\right)^{-5} = \left(\frac{2\times7}{6\times8}\right)^5$

Therefore, the correct equivalent expression is:

$\left(\frac{2\times7}{6\times8}\right)^5$

Hence, the choice corresponding to this expression is correct.

Therefore, the solution to the problem is $\left(\frac{2\times7}{6\times8}\right)^5$, which corresponds to choice 1.