Question

Apply the Properties of Integer Exponents to generate equivalent expressions to 37⋅3−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)

3^7⋅3^−9=

Answer 1

[AI-generated answer — Bot GPT 3.5]

To apply the properties of integer exponents, we can use the rule that states that when multiplying powers with the same base, we add the exponents.

So, 37⋅3^(-9) can be rewritten as (3^7)⋅(3^(-9)).

Using the rule mentioned earlier, we can add the exponents:

3^7⋅3^(-9) = 3^(7 + (-9))

Now, simplifying the exponent:

3^(7 + (-9)) = 3^(-2)

Therefore, 37⋅3^(-9) is equivalent to 3^(-2).

We can further simplify 3^(-2) by using another exponent property, which states that any non-zero number raised to the power of -n is equal to the reciprocal of that number raised to the power of n.

So, 3^(-2) is equivalent to 1/(3^2).

Since 3^2 equals 9, the simplified expression is:

1/9.

Answer 2

apply the properties of integer exponents to generate equivalent expressions to 2^2/2^−4 with only positive exponents, then solve the expression. provide the solution as a whole number.(1 point)

2^2/2^−4=

Answer 3

[AI-generated answer — Bot GPT 3.5]

To generate equivalent expressions with only positive exponents, we can use the rule that states that when dividing powers with the same base, we subtract the exponents.

So, 2^2/2^(-4) can be rewritten as (2^2)/(2^(-4)).

Using the rule mentioned earlier, we can subtract the exponents:

(2^2)/(2^(-4)) = 2^(2 - (-4))

Simplifying the exponent:

2^(2 - (-4)) = 2^(2 + 4)

2^(2 + 4) = 2^6

Therefore, 2^2/2^(-4) is equivalent to 2^6.

Simplifying 2^6, we get:

2^6 = 64

Hence, the solution to the expression 2^2/2^(-4) is 64.

Answer 4

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

To generate an equivalent expression with only positive exponents, you can use the property of integer exponents which states that for any positive integers a and b,

a^b ⋅ a^c = a^(b+c).

Using this property, we can rewrite the expression as:

37 ⋅ 3^(-9) = 3^7 ⋅ 3^(-9) = 3^(7+(-9)).

Since (-9) is negative, when we rewrite it, it becomes 1/9. Therefore,

3^7 ⋅ 3^(-9) = 3^(7+(-9)) = 3^(-2) or 1/3^2.

Simplifying further, we have:

3^(-2) = 1/3^2 = 1/9.

So, the simplified answer is 1/9.