Question

Simplify

4^13 divided by 3^-5

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

To simplify the expression \(4^{13} \div 3^{-5}\), we can first simplify each part separately.

We have \(4^{13}\), which means 4 multiplied by itself 13 times, and \(3^{-5}\), which means 1 divided by \(3^5\) (since a negative exponent indicates reciprocal).

First, let's deal with \(3^{-5}\):
\(3^{-5} = \frac{1}{3^5}\)

Now, let's deal with the division. Dividing by a fraction is the same as multiplying by its reciprocal. So we can write the expression as multiplication by the reciprocal of \(3^{-5}\):
\(4^{13} \div 3^{-5} = 4^{13} \times \frac{1}{3^{-5}}\)

And now, applying the reciprocal:

\(4^{13} \times 3^5\)

This can't be simplified further in terms of exact integer values unless we want to actually calculate the values of \(4^{13}\) and \(3^5\), which would result in an extremely large number. However, usually, we leave the expression in the exponential form to represent the exact value, which is:

\(4^{13} \times 3^5\)

This expression shows the simplified form of the original division problem. If you need the decimal or fractional form, you would have to calculate the values of \(4^{13}\) and \(3^5\) and then multiply them together.

Answer 2

Wrong

Simplify it as an answer, not an equation

Answer 3

[AI-generated answer — Bot GPT-4 Turbo]

Apologies for the misunderstanding.

To simplify the expression as a numerical answer, we can calculate the powers separately and then divide.

First, we calculate \(4^{13}\):
\[ 4^{13} = 4 \times 4 \times 4 \times \ldots \times 4 \] (13 times)

Then, we calculate \(3^{-5}\):
\[ 3^{-5} = \frac{1}{3^5} = \frac{1}{3 \times 3 \times 3 \times 3 \times 3} \]

To divide \(4^{13}\) by \(3^{-5}\), we multiply \(4^{13}\) by the reciprocal of \(3^{-5}\), which is \(3^5\):
\[ 4^{13} \div 3^{-5} = 4^{13} \times 3^5 \]

Next, we'll calculate the actual numbers for both expressions.

\( 4^{13} = 67,108,864 \) (calculated by raising 4 to the power of 13)

\( 3^5 = 243 \) (calculated by raising 3 to the power of 5)

Now, multiply these two results together:
\[ 67,108,864 \times 243 = 16,299,448,832 \]

Therefore, the simplified numerical answer is \( 16,299,448,832 \).

Answer 4

Simplify 16,299,448,832

Answer 5

[AI-generated answer — Bot GPT-4 Turbo]

The number 16,299,448,832 is already in its simplest form as an integer. However, it can be simplified further by expressing it in scientific notation, or by factoring it, if that's what you're looking for.

In scientific notation, 16,299,448,832 would be written as:

\( 1.6299448832 \times 10^{10} \)

If you're interested in prime factorization (i.e., expressing the number as a product of its prime factors), then you would need to find all the prime numbers that multiply together to give you 16,299,448,832. This is a large computation and generally is not done manually for numbers this large.

If you are looking for simplification in some other context, please specify.

Answer 6

[AI-generated answer — Explain Bot]

To simplify the expression 4^13 divided by 3^-5, we can use the rules of exponents.

First, let's simplify the numerator, which is 4^13. To do this, we multiply the base (4) by itself 13 times:

4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 = 67,108,864

Now, let's simplify the denominator, which is 3^-5. The negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent:

3^-5 = 1 / 3^5

To simplify 3^5, we multiply the base (3) by itself 5 times:

3 × 3 × 3 × 3 × 3 = 243

Now, we can substitute these values back into the expression:

(4^13) / (3^-5) = 67,108,864 / (1 / 243)

When dividing by a fraction, we can multiply by its reciprocal:

67,108,864 / (1 / 243) = 67,108,864 × 243

To multiply these two values, we simply multiply them together:

67,108,864 × 243 = 16,309,876,992

Therefore, the simplified expression is 16,309,876,992.