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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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GPT 3.5
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.
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.
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