Write with a single exponent:

1. \(\frac{7^6}{7^2}\)

2. \((11^4)^5\)

3. \(4^2 \boldcdot 4^6\)

4. \(6 \boldcdot 6^8\)

5. \((12^2)^7\)

6. \(\frac{3^{10}}{3}\)

7. \((0.173)^9 \boldcdot (0.173)^2\)

8. \(\frac{0.87^5}{0.87^3}\)

9. \(\frac{(\frac{5}{2})^8}{(\frac{5}{2})^6}\)

Determine whether each of the following equations is true or false? Explain or show your reasoning.

1. \((7^2)^3 = 7^5\)
2. \(2^4 \boldcdot 2 = 2^5\)
3. \(2^2 \boldcdot 3^4 = 6^6\)
4. \(( (\frac23)^2 )^4 = (\frac23)^8\)

Noah says that \(2^4 \boldcdot 3^2 = 6^6\). Tyler says that \(2^4 \boldcdot 4^2 = 16^2\).

1. Do you agree with Noah? Explain or show your reasoning.
2. Do you agree with Tyler? Explain or show your reasoning.

Lin says that the system of equations \(2x + 6y = 10\) and \(3x + 9y = 15\) has an infinite number of solutions.

1. Do you agree with Lin? Explain your reasoning.

2. Write a new equation that makes a system with infinite solutions together with \(2x + 6y = 10\). 

3. Describe the graph of the new system.