The image presents three math problems: 1. Evaluate $5^3 \times \frac{1}{5^2}$.

1. Problem Description

The image presents three math problems:

1. Evaluate $5^3 \times \frac{1}{5^2}$.

2. Expand and simplify $(2a + 3)(3a - 4)$.

3. Solve the equation $4x^2 = 9x$.

2. Solution Steps

Problem 1: Evaluate $5^3 \times \frac{1}{5^2}$.

We can rewrite the expression as:

$5^3 \times \frac{1}{5^2} = \frac{5^3}{5^2}$.

Using the property $\frac{a^m}{a^n} = a^{m-n}$, we have:

$\frac{5^3}{5^2} = 5^{3-2} = 5^1 = 5$.

Problem 2: Expand and simplify $(2a + 3)(3a - 4)$.

We use the distributive property (FOIL method):

$(2a + 3)(3a - 4) = 2a(3a) + 2a(-4) + 3(3a) + 3(-4)$

$= 6a^2 - 8a + 9a - 12$

$= 6a^2 + a - 12$.

Problem 3: Solve the equation $4x^2 = 9x$.

Subtract $9x$ from both sides:

$4x^2 - 9x = 0$.

Factor out $x$:

$x(4x - 9) = 0$.

So either $x = 0$ or $4x - 9 = 0$.

If $4x - 9 = 0$, then $4x = 9$, so $x = \frac{9}{4}$.

Thus, the solutions are $x = 0$ or $x = \frac{9}{4}$.

3. Final Answer

1. 5

2. $6a^2 + a - 12$

3. $x = 0$ or $x = \frac{9}{4}$