1 of 5

Question

1 of 5

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.

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3 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

To generate equivalent expressions with positive exponents, we can use the property of integer exponents that states:

a^m ⋅ a^n = a^(m+n)

Using this property, we can rewrite the expression 3^7⋅3^−9 as:
3^(7+(-9))

Simplifying the exponent, we get:
3^(-2)

To convert this to a positive exponent, we can use the property that states:
a^(-n) = 1/a^n

Applying this property to our expression, we get:
1/3^2

Simplifying further, we get:
1/9

Therefore, the simplified answer is 1/9.

Answer 2

Step-by-Step Bot answered
1 year ago

To apply the Properties of Integer Exponents to generate equivalent expressions with positive exponents for 3^7⋅3^−9, we can use the product rule, which states that when multiplying powers with the same base, we add the exponents.

Step 1: Apply the product rule
3^7⋅3^−9 = 3^(7 + -9)

Step 2: Simplify the exponent
3^(7 + -9) = 3^(-2)

To solve the expression 3^(-2), we can use the property that a negative exponent in a fraction can be written as a positive exponent in the denominator of the fraction.

Step 3: Rewrite the expression with a positive exponent
3^(-2) = 1/3^2

Step 4: Simplify the expression
1/3^2 = 1/9

Therefore, the simplified fraction, which is the solution to the expression 3^7⋅3^−9 with only positive exponents, is 1/9.

Answer 3

Explain Bot answered
1 year ago

To generate equivalent expressions with only positive exponents, we can use the properties of integer exponents. The properties that we will use are:

1. Product of Powers Property: When multiplying two powers with the same base, you add the exponents.
For example, x^m * x^n = x^(m+n).

2. Quotient of Powers Property: When dividing two powers with the same base, you subtract the exponents.
For example, x^m / x^n = x^(m-n).

Using these properties, we can rewrite the expression 3^7 * 3^(-9) with only positive exponents.

Step 1: Apply the Product of Powers Property.
3^7 * 3^(-9) = 3^(7 + (-9))

Step 2: Simplify the exponents.
3^(7 + (-9)) = 3^(-2)

Now that we have an expression with a positive exponent, we can solve it.

To solve 3^(-2), we use the definition of negative exponents:

x^(-n) = 1 / x^n

Step 3: Apply the definition of negative exponents.
3^(-2) = 1 / 3^2

Step 4: Simplify.
1 / 3^2 = 1 / 9

Therefore, the simplified fraction that solves the expression 3^7 * 3^(-9) is 1/9.