Apply the properties of integer exponents to generate equivalent expressions to 3^7 • 3^-9 with only positive exponent on South expression. Your answer will be simplified fraction with no remaining exponents.
To generate an equivalent expression with only positive exponents, we can use the property that says:
\[a^{-b} = \frac{1}{a^b}\]
Applying this property to the given expression, we have:
\[3^7 \cdot 3^{-9} = 3^{7+(-9)} = 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\]
So, the equivalent expression with only positive exponents is \(\frac{1}{9}\).
That’s incorrect
I apologize for the mistake. Let's correct it.
Using the property \(a^{m} \cdot a^{n} = a^{m+n}\), we can rewrite the expression as follows:
\[3^7 \cdot 3^{-9} = 3^{7+(-9)} = 3^{-2}\]
Now, using the property \(a^{-m} = \frac{1}{a^m}\), we can convert the negative exponent into a positive exponent:
\[3^{-2} = \frac{1}{3^2}\]
Simplifying the expression, we get:
\[\frac{1}{3^2} = \frac{1}{9}\]
So, the equivalent expression with only positive exponents is \(\frac{1}{9}\). I apologize for the confusion in my previous response.
That’s not right either.
I apologize for the mistake again. Let's correct it.
To apply the properties of integer exponents to generate an equivalent expression with only positive exponents for \(3^7 \cdot 3^{-9}\), we can use the property \(a^m \cdot a^n = a^{m+n}\).
So, \(3^7 \cdot 3^{-9}\) can be written as \(3^{7+(-9)}\) which simplifies to \(3^{-2}\).
To convert the negative exponent into a positive exponent, we can use the property \(a^{-m} = \frac{1}{a^m}\). Applying this property to \(3^{-2}\), we get \(\frac{1}{3^2}\).
Simplifying \(\frac{1}{3^2}\), we find that it is equal to \(\frac{1}{9}\).
Therefore, the equivalent expression with only positive exponents for \(3^7 \cdot 3^{-9}\) is \(\frac{1}{9}\).
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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 simplified fraction with no remaining exponents
To generate equivalent expressions with only positive exponents for \(3^7 \cdot 3^{-9}\), we can simplify using the properties of exponents:
First, apply the property \(a^{m} \cdot a^{n} = a^{m+n}\) to the given expression:
\(3^7 \cdot 3^{-9} = 3^{7+(-9)} = 3^{-2}\)
Next, use the property \(a^{-m} = \frac{1}{a^m}\) to convert the negative exponent into a positive exponent:
\(3^{-2} = \frac{1}{3^2}\)
Now, simplify the expression by evaluating \(3^2\) which gives us:
\(\frac{1}{3^2} = \frac{1}{9}\)
So the simplified fraction with no remaining exponents for \(3^7 \cdot 3^{-9}\) is \(\frac{1}{9}\).