What is the simplified expression for 3 raised to the power of 3 multiplied by 3 raised to the power of 3, all divided by 3 raised to the power of 4?

To simplify the expression \( \frac{3^3 \times 3^3}{3^4} \), we can follow the rules of exponents.

First, we can simplify the numerator:

  • \(3^3 \times 3^3 = 3^{3+3} = 3^6\) (using the property that when multiplying like bases, you add the exponents).

Now, our expression looks like this:

\( \frac{3^6}{3^4} \)

Next, we can simplify the fraction. According to the rules of exponents, when dividing like bases, we subtract the exponents:

  • \(3^6 \div 3^4 = 3^{6-4} = 3^2\)

Therefore, the simplified expression is:

\(3^2\)

Finally, calculating \(3^2\) gives us:

\(9\)

In summary, the simplified expression for \( \frac{3^3 \times 3^3}{3^4} \) is:

9

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