https://file.aiquickdraw.com/mathbot/file/17273160833939e4vfnad.jpg

Let's solve the two problems step by step.

### Problem 1: 
\[
(56^8) \times (56^{-10}) \times 56
\]

Using the property of exponents: \( a^m \times a^n = a^{m+n} \), we can simplify the expression:
\[
56^8 \times 56^{-10} \times 56 = 56^{8 + (-10) + 1}
\]
\[
= 56^{-1}
\]
Thus:
\[
56^{-1} = \frac{1}{56}
\]

So, the answer to the first problem is:
\[
\frac{1}{56}
\]

### Problem 2:
\[
\sqrt{700} + \sqrt{180} \times \sqrt{80} - \sqrt{847}
\]

First, let's break down each square root term:
\[
\sqrt{700} = \sqrt{100 \times 7} = 10\sqrt{7}
\]
\[
\sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5}
\]
\[
\sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5}
\]
\[
\sqrt{847} \text{ cannot be simplified further.}
\]

Now substitute these values into the expression:
\[
10\sqrt{7} + (6\sqrt{5}) \times (4\sqrt{5}) - \sqrt{847}
\]

Simplify the multiplication:
\[
(6\sqrt{5}) \times (4\sqrt{5}) = 24 \times 5 = 120
\]

Now the expression becomes:
\[
10\sqrt{7} + 120 - \sqrt{847}
\]

This is the simplified form. Further approximation would give numerical values for the square roots.

Do you want to approximate the final answer numerically or leave it in this simplified form?

---

Let me know if you'd like more details or have any questions! Here are five related questions to expand your understanding:

1. How do exponent rules apply when multiplying terms with negative exponents?
2. Can all square roots be simplified in the same way?
3. How do you handle square roots of numbers that cannot be simplified, such as \( \sqrt{847} \)?
4. Why is it useful to express square roots in terms of factors for simplification?
5. How does the distributive property of multiplication apply in square root expressions?

**Tip:** When simplifying expressions with exponents, always combine like terms to reduce the expression as much as possible!

Solve the following: 1. (56^8) * (56^-10) * 56  2. sqrt(700) + sqrt(180) * sqrt(80) - sqrt(847)

Learn how to solve exponentiation and square root problems. This guide walks through simplifying the expression (56^8) * (56^-10) * 56 and breaking down square roots such as sqrt(700), sqrt(180), and sqrt(847). Suitable for high school math students.

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