Apply All Exponent Rules Practice

Question

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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=

Remaining Attempts : 3

Answer 1

To simplify the expression \( 3^7 \cdot 3^{-9} \) using the properties of integer exponents, we can use the rule that states \( a^m \cdot a^n = a^{m+n} \).

1. Combine the exponents: \[ 3^7 \cdot 3^{-9} = 3^{7 + (-9)} = 3^{-2} \]

2. To express this with only positive exponents, recall that \( a^{-n} = \frac{1}{a^n} \): \[ 3^{-2} = \frac{1}{3^2} \]

3. Now, simplify \( 3^2 \): \[ \frac{1}{3^2} = \frac{1}{9} \]

Thus, the expression \( 3^7 \cdot 3^{-9} \) simplifies to: \[ \frac{1}{9} \]

The final answer without remaining exponents is: \[ \frac{1}{9} \]