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.
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.
To apply the property of negative integer exponents and generate an expression with positive exponents only, we can use the rule that says for any nonzero number a,
a^(-n) = 1 / (a^n)
Let's apply this rule to the expression 7^(-3) * 7^(-5):
7^(-3) * 7^(-5) = 1/(7^3) * 1/(7^5)
Using the rule mentioned above, we can rewrite each term with positive exponents:
1/(7^3) * 1/(7^5) = 1/(7^3) * 1/(7^2 * 7^3)
Now, using the product of powers rule (a^m * a^n = a^(m+n)), we can simplify further:
1/(7^3) * 1/(7^2 * 7^3) = 1/7^(3 + 2 + 3)
Adding the exponents, we get:
1/7^(8)
Therefore, the expression equivalent to 7^(-3) * 7^(-5) with positive exponents only is 1/7^(8).