Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^-3 * 7^-5

Answer 1

[AI-generated answer — Bot GPT 3.5]

To apply the property of negative integer exponents, we need to rewrite each term with a positive exponent.

First, we can rewrite 7^-3 as 1/7^3.

Similarly, we can rewrite 7^-5 as 1/7^5.

Now, we can multiply these two terms together:

1/7^3 * 1/7^5 = 1/(7^3 * 7^5)

To simplify further, we can add the exponents when multiplying powers with the same base:

1/(7^(3+5)) = 1/7^8

Therefore, the expression equivalent to 7^-3 * 7^-5 is 1/7^8.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To apply the property of negative integer exponents, we can rewrite the given expression using the rule that states:

a^(-m) = 1 / (a^m)

Applying this rule to the expression 7^(-3) * 7^(-5), we get:

1 / (7^3) * 1 / (7^5)

Simplifying further, we can combine the fractions:

1 / (7^3 * 7^5)

Now, we can use the rule that states:

a^m * a^n = a^(m+n)

Applying this rule to the expression 7^3 * 7^5, we get:

7^(3+5)

Simplifying, we have:

7^8

Therefore, the expression equivalent to 7^-3 * 7^-5 is 7^8.

Answer 3

[AI-generated answer — Explain Bot]

To apply the property of negative integer exponents, we need to remember the rule: a^(-n) = 1 / (a^n).

Let's start by rewriting the given expression using this rule:

7^-3 * 7^-5 = 1 / (7^3) * 1 / (7^5)

Now that we have written each exponent as a positive value, we can simplify further:

= 1 / (7^3) * 1 / (7^5)
= 1 / (7 * 7 * 7) * 1 / (7 * 7 * 7 * 7 * 7)

Now, let's combine the fractions by multiplying the numerator and the denominator:

= (1 * 1) / ((7 * 7 * 7 * 7 * 7) * (7 * 7 * 7))
= 1 / (7^8)

So, the expression equivalent to 7^-3 * 7^-5 is 1 / (7^8).