Question

give me a problem similiar to (7^5)^10times7^200/(7^-2)^30

Answer 1

so is this right?
7^250/7^-60
5^182/5^-60
Add denominater to the numerater by flipping its exponent so
5^182 times 5^60
So the solution is 5^242

Answer 2

To create a problem similar to \((7^5)^{10} \times 7^{200} / (7^{-2})^{30}\), we can modify the base and the exponents while keeping the structure of the expression intact.

Here's a similar problem:

\[
(5^4)^{8} \times 5^{150} / (5^{-3})^{20}
\]

In this problem, we've changed the base from \(7\) to \(5\), and adjusted the exponents accordingly to maintain a similar structure.

Answer 3

Let's break down the expression you provided step by step to verify it.

You are starting with the expression:

\[
\frac{7^{250}}{7^{-60}}
\]

Using the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we can simplify it:

\[
7^{250 - (-60)} = 7^{250 + 60} = 7^{310}
\]

Now, let's also look at the second part of your calculations, which appears to be a separate expression:

\[
\frac{5^{182}}{5^{-60}}
\]

Using the same property of exponents:

\[
5^{182 - (-60)} = 5^{182 + 60} = 5^{242}
\]

So, your final answer of \(5^{242}\) from the second expression is correct.

Each expression simplifies individually, with \(7^{310}\) and \(5^{242}\) being their respective results. But you should ensure you are working with the correct terms as you combine or analyze different problems.

To summarize:

1. \(\frac{7^{250}}{7^{-60}} = 7^{310}\)
2. \(\frac{5^{182}}{5^{-60}} = 5^{242}\)

Both steps are correct for the respective expressions.