simplify 4 with an exponent of 13 divided by 3 with an exponent of -5

Answer 1

To simplify the expression \( \frac{4^{13}}{3^{-5}} \), we can start by recalling that dividing by a negative exponent is equivalent to multiplying by the positive exponent:

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

Now, we can express it as:

\[ 4^{13} \cdot 3^{5} \]

At this point, there isn't a standard way to simplify \( 4^{13} \cdot 3^{5} \) further without calculating the actual numerical values. However, if you need it in terms of powers, it can just remain as:

\[ 4^{13} \cdot 3^{5} \]

If you would like to calculate the numerical value:

1. Calculate \( 4^{13} \).
2. Calculate \( 3^{5} \).
3. Multiply the two results.

Calculating these:

• \( 4^{13} = 67,108,864 \)
• \( 3^{5} = 243 \)

So,

\[ 4^{13} \cdot 3^{5} = 67,108,864 \cdot 243 = 16,349,249,152 \]

Thus, the simplified expression is either \( 4^{13} \cdot 3^{5} \) or its numerical value \( 16,349,249,152 \).

Answer 2

what is the simplified version

Answer 3

The expression \( \frac{4^{13}}{3^{-5}} \) simplifies to:

\[ 4^{13} \cdot 3^{5} \]

This is the simplified version in terms of powers. If you're looking for a numerical representation, we can compute it as follows:

1. \( 4^{13} = 67,108,864 \)
2. \( 3^{5} = 243 \)

Now, multiplying these two results gives:

\[ 4^{13} \cdot 3^{5} = 67,108,864 \cdot 243 = 16,349,249,152 \]

Thus, the expression \( \frac{4^{13}}{3^{-5}} \) can be kept in its simplified form as \( 4^{13} \cdot 3^{5} \) or, if needed, expressed numerically as \( 16,349,249,152 \).

So, the simplified form of the expression is:

\[ 4^{13} \cdot 3^{5} \]

This is the standard way to express it without further numerical calculation.

Answer 4

thats incorrect

Answer 5

I apologize for any confusion in my response. Let's go through the simplification of the expression \( \frac{4^{13}}{3^{-5}} \) correctly step by step.

1. Understanding the expression: The expression \( \frac{4^{13}}{3^{-5}} \) can be rewritten using the property of negative exponents: \[ \frac{a}{b^{-c}} = a \cdot b^{c} \] Therefore, \[ \frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5} \]

2. Final simplified form: As mentioned earlier, this is already in a simplified form, but if you need it shown with the bases combined (if possible) or simplified further, we look at it this way: \[ 4^{13} \cdot 3^{5} \]

   • However, there is no further simplification in terms of a single expression since \( 4 \) and \( 3 \) cannot be combined due to differing bases.

So the correct simplified version of the expression \( \frac{4^{13}}{3^{-5}} \) is indeed:

\[ 4^{13} \cdot 3^{5} \]

If we convert this into numerical values for clarity:

• \( 4^{13} = 67,108,864 \)
• \( 3^{5} = 243 \)

The numerical value of the multiplication is:

\[ 67,108,864 \cdot 243 = 16,349,249,152 \]

However, if we are strictly simplifying the expression, the answer remains:

\[ 4^{13} \cdot 3^{5} \]

Please let me know if you are looking for something different. Thank you for your understanding!

Answer 6

no its not its wrong bot

Answer 7

I apologize for any confusion earlier. Let's go through the simplification step by step correctly.

You started with the expression:

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

Applying the property of negative exponents, we can rewrite this as:

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

Now we can write \(4^{13}\) in terms of its prime factorization. Since \(4 = 2^2\), we have:

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

So, replacing \(4^{13}\) in our expression gives us:

\[ 2^{26} \cdot 3^{5} \]

This is the simplified form of the original expression. There is no further simplification possible without evaluating the numerical values.

So the final simplified version is:

\[ 2^{26} \cdot 3^{5} \]

Thank you for your patience, and I hope this addresses your query correctly!