Quention 3 3.1.1 $$ -4 x^{2} y^{3} imes\left(-3 x^{2} y^{-5} ight) $$ (2) $$ (5 y)^{0} $$ 3.1.3 $$ \frac{(2 x-2)-2}{2 x^{3}} $$ $$ 3.25 y^{3} x $$

Question

Quention 3 3.1.1 $$ -4 x^{2} y^{3} 	imes\left(-3 x^{2} y^{-5}ight) $$ (2) $$ (5 y)^{0} $$ 3.1.3 $$ \frac{(2 x-2)-2}{2 x^{3}} $$ $$ 3.25 y^{3} x $$

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Solution:
  $$3.25y^{3}x$$
Calculate or simplify the expression $$ -4*x^2*y^3*(-3*x^2*y^(-5)) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$-4x^{2}y^{3}\left(-3x^{2}y^{-5}\right)$$
- step1: Rewrite the expression:
  $$-4x^{2}y^{3}\left(-3\right)x^{2}y^{-5}$$
- step2: Rewrite the expression:
  $$4x^{2}y^{3}\times 3x^{2}y^{-5}$$
- step3: Multiply the terms:
  $$12x^{2}y^{3}x^{2}y^{-5}$$
- step4: Multiply the terms:
  $$12x^{2+2}y^{3}\times y^{-5}$$
- step5: Add the numbers:
  $$12x^{4}y^{3}\times y^{-5}$$
- step6: Multiply the terms:
  $$12x^{4}y^{3-5}$$
- step7: Subtract the numbers:
  $$12x^{4}y^{-2}$$
- step8: Simplify:
  $$\frac{12x^{4}}{y^{2}}$$
Calculate or simplify the expression $$ (5*y)^0 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(5y\right)^{0}$$
- step1: Simplify:
  $$1$$
Calculate or simplify the expression $$ ((2*x-2)-2)/(2*x^3) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(\left(2x-2\right)-2\right)}{2x^{3}}$$
- step1: Remove the parentheses:
  $$\frac{\left(2x-2\right)-2}{2x^{3}}$$
- step2: Remove the parentheses:
  $$\frac{2x-2-2}{2x^{3}}$$
- step3: Subtract the numbers:
  $$\frac{2x-4}{2x^{3}}$$
- step4: Factor:
  $$\frac{2\left(x-2\right)}{2x^{3}}$$
- step5: Reduce the fraction:
  $$\frac{x-2}{x^{3}}$$
Let's solve each part step by step:

### 3.1.1 
We need to simplify the expression:
$$
-4 x^{2} y^{3} \times (-3 x^{2} y^{-5})
$$

**Step 1:** Multiply the coefficients:
$$
-4 \times -3 = 12
$$

**Step 2:** Combine the $$x$$ terms:
$$
x^{2} \times x^{2} = x^{4}
$$

**Step 3:** Combine the $$y$$ terms:
$$
y^{3} \times y^{-5} = y^{3 - 5} = y^{-2}
$$

**Final Result:**
$$
12 x^{4} y^{-2} = \frac{12 x^{4}}{y^{2}}
$$

### 3.1.2 
We need to simplify:
$$
(5 y)^{0}
$$

According to the zero exponent rule, any non-zero number raised to the power of zero is 1.

**Final Result:**
$$
1
$$

### 3.1.3 
We need to simplify:
$$
\frac{(2 x - 2) - 2}{2 x^{3}}
$$

**Step 1:** Simplify the numerator:
$$
(2 x - 2) - 2 = 2 x - 4
$$

**Step 2:** Write the expression:
$$
\frac{2 x - 4}{2 x^{3}}
$$

**Step 3:** Factor the numerator:
$$
\frac{2(x - 2)}{2 x^{3}} = \frac{x - 2}{x^{3}}
$$

**Final Result:**
$$
\frac{x - 2}{x^{3}}
$$

### 3.1.4 
The expression is:
$$
3.25 y^{3} x
$$

This expression is already in its simplest form.

**Final Result:**
$$
3.25 y^{3} x
$$

### Summary of Results:
1. $$ \frac{12 x^{4}}{y^{2}} $$
2. $$ 1 $$
3. $$ \frac{x - 2}{x^{3}} $$
4. $$ 3.25 y^{3} x $$
1. $$ \frac{12 x^{4}}{y^{2}} $$ 2. $$ 1 $$ 3. $$ \frac{x - 2}{x^{3}} $$ 4. $$ 3.25 y^{3} x $$

Quention 3
3.1.1
(2)

3.1.3

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Quention 3 3.1.1 (2) 3.1.3