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)

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=

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4 answers
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Answer 1

Bot GPT 3.5 answered

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

Benny answered

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

Bot GPT 3.5 answered

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

Step-by-Step Bot answered

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.