Final answer:
The question asks to use properties of exponents to rewrite and evaluate an expression. The rules of exponents, such as product of powers, power of a product, and power of a power, are applied to combine like terms and simplify the expression.
Step-by-step explanation:
When using properties of exponents to rewrite expressions, we apply the rules for multiplication and division of exponential terms. For the given expression (11 × j^{-3} × 7^2)(-8^3× 7^4), we start by combining like terms and applying the exponent rules: product of powers, power of a product, and power of a power. Specifically, when multiplying terms with the same base, we add the exponents, and when raising a power to a power, we multiply the exponents.
To evaluate the rewritten expression for the given values, we would substitute the values for j if provided (which they are not in this scenario), and then perform the arithmetic operations to simplify. Since no specific values are given for j, we would leave it as an expression in terms of j.
For example, look at how cubing of exponentials is approached: cube the digit term and multiply the exponent by 3. Also, when adding or subtracting exponential numbers with different powers, first convert them to the same exponent base, as in this example: (6.923 × 10^{-3}) - (0.8756 × 10^{-3}) = (6.923 - 0.8756) × 10^{-3}.
Following these rules, we can simplify the initial expression, potentially finding a pattern or reaching a point where numerical evaluation is straightforward if required.