Question

Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7⋅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 add the exponents when multiplying powers with the same base.

3^7⋅3^−9 = 3^(7+(-9)) = 3^(-2)

To convert the expression to have only positive exponents, we can use the property a^(-n) = 1/a^n.

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

Therefore, the simplified equivalent 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 apply the properties of integer exponents, we can subtract the exponents when dividing powers with the same base.

2^2/2^(-4) = 2^(2-(-4)) = 2^(2+4) = 2^6

Therefore, the simplified expression with only positive exponents is 2^6.

Solving 2^6, we know that 2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64.

Therefore, the solution as a whole number is 64.

Answer 4

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

To generate equivalent expressions with only positive exponents, we can use the properties of integer exponents. According to the product rule, when multiplying two numbers with the same base, we add their exponents.

Using this rule, we can rewrite 3^7⋅3^−9 as:

3^(7 + -9)

Simplifying the exponent, we get:

3^(-2)

To convert this expression to an equivalent expression with only positive exponents, we can use the property that states any number raised to a negative exponent can be rewritten as the reciprocal of that number raised to the positive exponent.

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

Simplifying further, we have:

1 / (3^2) = 1 / 9

Therefore, the solution to the expression 3^7⋅3^−9 is 1/9.