Let's break down the content from the image you uploaded. It looks like you have two parts:

1. Solve the equation:

$3^{5x + 3} = 81$ We need to find the value of $x$.

Solution:

First, express $81$ as a power of 3: $81 = 3^4$ So, the equation becomes: $3^{5x + 3} = 3^4$ Since the bases are the same (both base 3), we can set the exponents equal to each other: $5x + 3 = 4$ Now, solve for $x$: $5x = 4 - 3$ $5x = 1$ $x = \frac{1}{5}$

2. Simplify the expression:

$\frac{7^6 \times 7^{-3}}{7^4}$ We can simplify this step by step:

• Use the property of exponents: $a^m \times a^n = a^{m+n}$. $7^6 \times 7^{-3} = 7^{6-3} = 7^3$ Now, we have: $\frac{7^3}{7^4}$
• Use the property of exponents: $\frac{a^m}{a^n} = a^{m-n}$. $\frac{7^3}{7^4} = 7^{3-4} = 7^{-1}$

So, the simplified result is: $7^{-1} = \frac{1}{7}$

Would you like any further clarification or details on these steps? Here are some related questions you might find helpful:

1. How to solve equations involving exponential terms?
2. What are the properties of exponents?
3. Can you explain logarithms and how they relate to exponents?
4. How do you simplify rational expressions with exponents?
5. What is the relationship between exponents and logarithms?

Tip: When dealing with equations involving exponents, always try to express both sides with the same base to easily compare the exponents.