Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7−^3⋅7−^5 with positive exponents only
To apply the Property of Negative Integer Exponents and generate an expression with positive exponents only, we can rewrite 7^(-3) as 1/(7^3) and 7^(-5) as 1/(7^5).
So, the expression 7^(-3) ⋅ 7^(-5) can be rewritten as (1/(7^3)) ⋅ (1/(7^5)).
Using the property of exponents for multiplying, we know that when we multiply two expressions with the same base, we can add their exponents.
Therefore, (1/(7^3)) ⋅ (1/(7^5)) is equal to 1/(7^(3+5)).
Simplifying the exponent, we get 1/(7^8).
So, after applying the Property of Negative Integer Exponents, the expression 7^(-3) ⋅ 7^(-5) is equivalent to 1/(7^8), which has a positive exponent only.
To apply the Property of Negative Integer Exponents and generate an expression equivalent to 7^-3 ⋅ 7^-5 with positive exponents only, we can use the fact that a^(-n) = 1 / a^n.
Let's simplify the given expression step by step:
1. 7^-3 ⋅ 7^-5
Apply the property: 7^-3 = 1 / 7^3 and 7^-5 = 1 / 7^5
2. (1 / 7^3) ⋅ (1 / 7^5)
Now, applying the property of multiplication of fractions, we multiply the numerators and multiply the denominators:
3. (1 / 7^3) ⋅ (1 / 7^5) = 1 / (7^3 ⋅ 7^5)
Since the bases (7) are the same, we can simplify the expression further by adding the exponents:
4. 1 / (7^(3+5)) = 1 / 7^8
Therefore, the expression 7^-3 ⋅ 7^-5 with positive exponents only is equivalent to 1 / 7^8.
To apply the Property of Negative Integer Exponents, we can rewrite a negative exponent as its reciprocal with a positive exponent. The property states that a^(-n) is equal to 1/a^n.
Let's rewrite the expression 7^(-3) ⋅ 7^(-5) using this property:
7^(-3) ⋅ 7^(-5)
= 1/7^3 ⋅ 1/7^5 (using the Property of Negative Exponents)
Now, we can multiply the two fractions and simplify:
= (1/7^3) ⋅ (1/7^5)
= 1/(7^3 ⋅ 7^5) (using the property of multiplying fractions)
= 1/7^(3+5) (using the property of multiplying exponents)
= 1/7^8
So, the expression equivalent to 7^(-3) ⋅ 7^(-5) with positive exponents only is 1/7^8.