Apply the Property of negative integer exponents to generate an expression equivalent to 7 to the power of -3 times 7 to the power of -5 with positive exponents only.

Answer 1

The property of negative integer exponents states that a number raised to a negative exponent is equal to its reciprocal raised to the positive exponent. Therefore, the expression 7^(-3) can be rewritten as 1/7^3, and the expression 7^(-5) can be rewritten as 1/7^5.

Using this property, we can rewrite the given expression as (1/7^3) * (1/7^5).

To simplify the expression, we can combine the two fractions by multiplying the numerators and the denominators. Multiplying the numerators gives us 1 * 1, which is 1. Multiplying the denominators gives us 7^3 * 7^5, which can be simplified using the property of exponents that states when multiplying with the same base, you add the exponents.

Therefore, 7^3 * 7^5 simplifies to 7^(3+5) = 7^8.

The final expression is 1/(7^8). This is an equivalent expression with positive exponents only.