Solve ((4×6)/(5×10))^(-6): Negative Exponent Practice

Insert the corresponding expression:

$$$\left(\frac{4\times6}{5\times10}\right)^{-6}=$

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

• Step 1: Simplify the original expression inside the parentheses.
• Step 2: Apply the negative exponent to each factor in the fraction.
• Step 3: Use exponent rules to rewrite the expression.

Now, let's work through each step:
Step 1: The original expression is $\left(\frac{4 \times 6}{5 \times 10}\right)^{-6}$. Simplifying inside the fraction gives us $\frac{24}{50}$. However, we will work with the original form for clarity.
Step 2: Apply the exponent of $-6$ to each factor separately. This means $(4\times6)^{-6}$ in the numerator and $(5\times10)^{-6}$ in the denominator.
Step 3: Use the rule $(ab)^n = a^n \times b^n$. Thus, we have: $(4 \times 6)^{-6} = 4^{-6} \times 6^{-6}$ $(5 \times 10)^{-6} = 5^{-6} \times 10^{-6}$ Combining these gives the full expression: $\frac{4^{-6} \times 6^{-6}}{5^{-6} \times 10^{-6}}$

Therefore, the simplified form of the given expression and the correct choice is $\frac{4^{-6} \times 6^{-6}}{5^{-6} \times 10^{-6}}$.