https://file.aiquickdraw.com/mathbot/file/17270318546995toc9pau.jpg

Let's start by simplifying the expressions one by one from the image:

### 1. Simplify the expressions (Question 5):
#### a) \( 5x^4 \cdot (3x^2) \)
- \( 5x^4 \cdot 3x^2 = 15x^{4+2} = 15x^6 \)

#### b) \( -2x^3 \cdot (3x^4) \)
- \( -2x^3 \cdot 3x^4 = -6x^{3+4} = -6x^7 \)

#### c) \( 4x^5 \cdot \left(-\frac{3}{2}x\right) \)
- \( 4x^5 \cdot \left(-\frac{3}{2}x\right) = -\frac{12}{2}x^{5+1} = -6x^6 \)

#### d) \( 3x^3 y^2 \cdot (-2x^4 y^3) \)
- \( 3x^3 y^2 \cdot (-2x^4 y^3) = -6x^{3+4} y^{2+3} = -6x^7 y^5 \)

#### ε) \( -2x^2 y \cdot \left(-\frac{5}{4} xy^3 \right) \)
- \( -2x^2 y \cdot \left(-\frac{5}{4} xy^3 \right) = \frac{10}{4}x^{2+1}y^{1+3} = \frac{5}{2}x^3 y^4 \)

#### στ) \( (3x^4)^2 \)
- \( (3x^4)^2 = 9x^{4\cdot2} = 9x^8 \)

#### θ) \( (2x^3 y^2)^5 \)
- \( (2x^3 y^2)^5 = 2^5 x^{3\cdot5} y^{2\cdot5} = 32x^{15} y^{10} \)

#### ι) \( \left( -\frac{3}{2} xy^3 \right)^3 \)
- \( \left( -\frac{3}{2} xy^3 \right)^3 = -\frac{27}{8} x^3 y^9 \)

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### 2. Solve for \( A \) when \( x = -2 \) and \( y = 4 \) (Question 6):
Given expression for \( A \):
\[
A = \frac{(x^2 y^{-3})^3 \cdot (x^3 y)^{-1}}{(x^8 y^{-1})^{-2}}
\]
We need to substitute \( x = -2 \) and \( y = 4 \). Let me solve this step-by-step.

I'll calculate this now.The value of \( A \) when \( x = -2 \) and \( y = 4 \) is \( -0.03125 \).

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Would you like more details on any specific part of the solution or to proceed with the next set of questions?

Here are 5 related problems for further practice:
1. Simplify: \( (4x^2y)^4 \cdot (2x^{-3}y^5)^2 \)
2. Find the value of \( A = \frac{(x^3 y^{-2})^2}{(x^{-1} y^4)^3} \) when \( x = 3 \) and \( y = 2 \).
3. Simplify: \( (2x^5 y^2)^4 \cdot \left(-\frac{3}{x^3 y}\right)^2 \)
4. Solve for \( B = \frac{(x^{-3} y^2)^2}{(x^2 y^{-3})^3} \) for given \( x \) and \( y \).
5. Simplify: \( \left(-\frac{4}{3}x^2 y^{-3}\right)^3 \cdot \left(\frac{3}{x^4}\right)^2 \)

**Tip**: When simplifying exponents, remember that powers of products and powers of quotients are distributed to each term separately.

Simplify the expressions and solve for A when x = -2 and y = 4.

Learn how to simplify algebraic expressions with exponents and solve for A when x = -2 and y = 4. This problem covers key algebraic concepts such as exponentiation, multiplication of powers, and substitution. Suitable for students in Grades 9-11.

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