Simplify 1/((10×7)^5): Fraction with Compound Base Expression

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

• Step 1: Recognize the given expression: $\frac{1}{(10 \times 7)^5}$.

• Step 2: Apply the rule of negative exponents, which states: $\frac{1}{a} = a^{-1}$.

• Step 3: Express the reciprocal with a negative exponent: $\frac{1}{(10 \times 7)^5} = (10 \times 7)^{-5}$.

Now, let's further simplify the expression:
Given that $(a \times b)^n = a^n \times b^n$, we can rewrite $(10 \times 7)^5$ as $10^5 \times 7^5$. Thus, $(10 \times 7)^{-5} = (10^5 \times 7^5)^{-1} = 10^{-5} \times 7^{-5} = (10 \times 7)^{-5}$.

Therefore, the solution to the problem in the expression form is: $\left(10 \times 7\right)^{-5}$.