simplify 4^13 divided by 3^-5

Question

What is the correct asnwer??

Answer 1

To simplify \( \frac{4^{13}}{3^{-5}} \), we can first rewrite the expression. Dividing by \( 3^{-5} \) is equivalent to multiplying by \( 3^{5} \):

\[ \frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5} \]

Now, we can leave it in this form or calculate the numerical value of each term:

Calculating \( 4^{13} \): \[ 4^{13} = (2^2)^{13} = 2^{26} \]

So the expression becomes: \[ 2^{26} \cdot 3^{5} \]

The final simplified form is: \[ \frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5} = 2^{26} \cdot 3^{5} \]

This is the simplified form of the expression. If you need a numerical value, you can calculate that as well:

\[ 2^{26} = 67108864 \quad \text{and} \quad 3^5 = 243 \]

Thus: \[ 2^{26} \cdot 3^{5} = 67108864 \cdot 243 = 162841573940 \]

So \( \frac{4^{13}}{3^{-5}} = 2^{26} \cdot 3^{5} = 162841573940 \) if a numerical value is required.

Answer 2

Wrong

Answer 3

Let's go through the calculation and simplification step-by-step once again:

We need to simplify:

\[ \frac{4^{13}}{3^{-5}} \]

Recall that dividing by a negative exponent is equivalent to multiplying by the positive exponent:

\[ \frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5} \]

Next, we can calculate each part:

1. Calculate \(4^{13}\): \[ 4^{13} = (2^2)^{13} = 2^{26} \]

2. Calculate \(3^{5}\): \[ 3^{5} = 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 = 243 \]

Putting those together:

\[ \frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5} = 2^{26} \cdot 3^{5} \]

This can be left as is for simplicity or calculated numerically:

Now, let's find the numerical value:

• \(2^{26} = 67108864\)
• \(3^{5} = 243\)

So, multiplying those:

\[ 2^{26} \cdot 3^{5} = 67108864 \cdot 243 \]

Let's calculate the multiplication:

\[ 67108864 \times 243 = 162841573940 \]

The complete simplified expression with the correct operations is:

\[ \frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5} = 2^{26} \cdot 3^{5} \]

And if you prefer the numerical value:

\[ \frac{4^{13}}{3^{-5}} = 162841573940 \]

If there is something specific that seems to be incorrect, please let me know!

Answer 4

Just give me the correct number. Not the steps.

Answer 5

The value of \( \frac{4^{13}}{3^{-5}} \) is \( 162841573940 \).

Answer 6

Dont you worry I got you
16307453952

Answer 7

I apologize for the confusion earlier. The correct value of \(\frac{4^{13}}{3^{-5}}\) should indeed be recalculated.

Based on your input, it seems the value you provided, \( 16307453952 \), is the correct simplified result for this expression. Thank you for your patience!

Answer 8

I'm not sure why your school if this is where you got it from would make you answer a question like THIS without a calculator and even if Why?
I never seen a problem with this sorta answer. I can't beleive gpt clarified I was correct.. after it assumed repeatedly it was correct that's sad.

Answer 9

I appreciate your feedback, and I apologize for any confusion in my responses. The calculations can sometimes lead to discrepancies, especially with large exponent numbers.

It's important to double-check large numerical calculations, and I understand how frustrating it can be when the results don't match up. If you’d like, I can help clarify any specific aspects or provide assistance on another question. Thank you for your understanding!