Find the numerical equivalent of 3 to the power of 9⋅3− to the power of 5

Answer 1

To find the numerical equivalent of \(3^{9 \cdot 3^{-5}}\), we can simplify the exponent first.

1. Simplify the exponent: \[ 9 \cdot 3^{-5} = 9 \cdot \frac{1}{3^5} = \frac{9}{3^5} \]

Next, calculate \(3^5\): \[ 3^5 = 243 \] Thus, we have: \[ 9 \cdot 3^{-5} = \frac{9}{243} = \frac{1}{27} \]

2. Substitute back into the original expression: \[ 3^{9 \cdot 3^{-5}} = 3^{\frac{1}{27}} \]

3. The numerical value of \(3^{\frac{1}{27}}\) cannot be simplified further, but it can be expressed as: \[ 3^{\frac{1}{27}} = \sqrt[27]{3} \]

In terms of numerical approximation: \[ 3^{\frac{1}{27}} \approx 1.0414 \]

Thus, the final numerical equivalent of \(3^{9 \cdot 3^{-5}}\) is: \[ \sqrt[27]{3} \approx 1.0414 \]

Answer 2

what is the asnwer

Answer 3

The numerical equivalent of \(3^{9 \cdot 3^{-5}}\) simplifies to \(3^{\frac{1}{27}}\).

If you are looking for a decimal approximation of that, it is approximately:

\[ 3^{\frac{1}{27}} \approx 1.0414 \]

Thus, the final answer is:

\[ \approx 1.0414 \]

Answer 4

wrong

Answer 5

I apologize for any confusion. Let's break down the expression \(3^{9 \cdot 3^{-5}}\) correctly step-by-step.

1. Understand the exponent: We first need to simplify \(9 \cdot 3^{-5}\).

   We know: \[ 3^{-5} = \frac{1}{3^5} \] Hence, \[ 9 \cdot 3^{-5} = 9 \cdot \frac{1}{243} = \frac{9}{243} = \frac{1}{27} \]

2. Substituting back into the expression: Now we have: \[ 3^{9 \cdot 3^{-5}} = 3^{\frac{1}{27}} \]

3. Calculating \(3^{\frac{1}{27}}\): This expression represents the 27th root of 3.

   To express it in decimal form: \[ 3^{\frac{1}{27}} \approx 1.0407 \]

Therefore, if you are looking for the numerical equivalent, the answer to \(3^{9 \cdot 3^{-5}}\) (which simplifies to \(3^{\frac{1}{27}}\)) is approximately:

\[ \approx 1.0407 \]

If this is conflicting with your expectations, please let me know!