5. Write $$ \frac{3 a b^{2}}{8 x y} imes \frac{16 x y^{2}}{21 a b^{3}} $$ in its simplified forn and substitute the values to evaluate, given that $$ b=1 $$ and $$ y=2 $$. 6. Write $$ \frac{4 a x+8 x}{3 x-1} \div \frac{a+2}{6 x-2} $$ in its simplified form and substitute the value to evaluate, given that $$ x=-1 $$ and $$ a=2 $$. 7. Write $$ \frac{36 m^{2} n^{3}}{8 m} \div \frac{n^{2} m^{2}}{4 m n^{3}} $$ in its simplest form and substitute the values to evaluate, given that $$ m=3 $$ and $$ n=\frac{1}{3} $$ 8. Write $$ \frac{3 x^{2}+6 x}{2 x y+4 y} imes \frac{2 y}{9 x^{2}} $$ in its simplified form and substitute the value to evaluate, given that $$ x=1 $$ and $$ y=2 $$.

Question

5. Write $$ \frac{3 a b^{2}}{8 x y} 	imes \frac{16 x y^{2}}{21 a b^{3}} $$ in its simplified forn and substitute the values to evaluate, given that $$ b=1 $$ and $$ y=2 $$. 6. Write $$ \frac{4 a x+8 x}{3 x-1} \div \frac{a+2}{6 x-2} $$ in its simplified form and substitute the value to evaluate, given that $$ x=-1 $$ and $$ a=2 $$. 7. Write $$ \frac{36 m^{2} n^{3}}{8 m} \div \frac{n^{2} m^{2}}{4 m n^{3}} $$ in its simplest form and substitute the values to evaluate, given that $$ m=3 $$ and $$ n=\frac{1}{3} $$ 8. Write $$ \frac{3 x^{2}+6 x}{2 x y+4 y} 	imes \frac{2 y}{9 x^{2}} $$ in its simplified form and substitute the value to evaluate, given that $$ x=1 $$ and $$ y=2 $$.

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Solution:
  $$\frac{3ab^{2}}{8xy}\times \frac{16xy^{2}}{21ab^{3}}$$
- step1: Reduce the fraction:
  $$1\times \frac{2y}{7b}$$
- step2: Multiply the terms:
  $$\frac{2y}{7b}$$
Calculate or simplify the expression $$ \frac{3 x^{2}+6 x}{2 x y+4 y} \times \frac{2 y}{9 x^{2}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{3x^{2}+6x}{2xy+4y}\times \frac{2y}{9x^{2}}$$
- step1: Divide the terms:
  $$\frac{3x}{2y}\times \frac{2y}{9x^{2}}$$
- step2: Reduce the fraction:
  $$1\times \frac{1}{3x}$$
- step3: Multiply the terms:
  $$\frac{1}{3x}$$
Calculate or simplify the expression $$ \frac{36 m^{2} n^{3}}{8 m} \div \frac{n^{2} m^{2}}{4 m n^{3}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{36m^{2}n^{3}}{8m}\div \frac{n^{2}m^{2}}{4mn^{3}}$$
- step1: Multiply by the reciprocal:
  $$\frac{36m^{2}n^{3}}{8m}\times \frac{4mn^{3}}{n^{2}m^{2}}$$
- step2: Divide the terms:
  $$\frac{9mn^{3}}{2}\times \frac{4mn^{3}}{n^{2}m^{2}}$$
- step3: Divide the terms:
  $$\frac{9mn^{3}}{2}\times \frac{4n}{m}$$
- step4: Reduce the fraction:
  $$9n^{3}\times 2n$$
- step5: Multiply the numbers:
  $$18n^{3}\times n$$
- step6: Multiply the terms:
  $$18n^{4}$$
Calculate or simplify the expression $$ \frac{4 a x+8 x}{3 x-1} \div \frac{a+2}{6 x-2} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{4ax+8x}{3x-1}\div \frac{a+2}{6x-2}$$
- step1: Multiply by the reciprocal:
  $$\frac{4ax+8x}{3x-1}\times \frac{6x-2}{a+2}$$
- step2: Rewrite the expression:
  $$\frac{4x\left(a+2\right)}{3x-1}\times \frac{6x-2}{a+2}$$
- step3: Reduce the fraction:
  $$\frac{4x}{3x-1}\times \left(6x-2\right)$$
- step4: Rewrite the expression:
  $$\frac{4x}{3x-1}\times 2\left(3x-1\right)$$
- step5: Reduce the fraction:
  $$4x\times 2$$
- step6: Multiply the terms:
  $$8x$$
Substitute $$ x=-1,a=2 $$ into the expression $$ 8x $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$8x$$
- step1: Substitute:
  $$8\left(-1\right)$$
- step2: Simplify:
  $$-8$$
Substitute $$ m=3,n=\frac{1}{3} $$ into the expression $$ 18n^{4} $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$18n^{4}$$
- step1: Substitute:
  $$18\left(\frac{1}{3}\right)^{4}$$
- step2: Evaluate the power:
  $$18\times \frac{1}{81}$$
- step3: Multiply:
  $$\frac{2}{9}$$
Substitute $$ x=1,y=2 $$ into the expression $$ \frac{1}{3x} $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$\frac{1}{3x}$$
- step1: Substitute:
  $$\frac{1}{3\times 1}$$
- step2: Multiply:
  $$\frac{1}{3}$$
Substitute $$ b=1,y=2 $$ into the expression $$ \frac{2y}{7b} $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$\frac{2y}{7b}$$
- step1: Substitute:
  $$\frac{2\times 2}{7\times 1}$$
- step2: Multiply the numbers:
  $$\frac{4}{7\times 1}$$
- step3: Multiply:
  $$\frac{4}{7}$$
Let's solve each of the problems step by step.

### Problem 5
We need to simplify the expression:
$$
\frac{3 a b^{2}}{8 x y} \times \frac{16 x y^{2}}{21 a b^{3}}
$$

**Step 1: Simplify the expression**
$$
= \frac{3 \cdot 16 \cdot a \cdot b^{2} \cdot x \cdot y^{2}}{8 \cdot 21 \cdot a \cdot b^{3} \cdot x \cdot y}
$$
Cancelling out common terms:
$$
= \frac{48 b^{2} y}{168 b^{3}} = \frac{2y}{7b}
$$

**Step 2: Substitute values $$ b=1 $$ and $$ y=2 $$**
$$
\frac{2 \cdot 2}{7 \cdot 1} = \frac{4}{7}
$$

### Problem 6
We need to simplify the expression:
$$
\frac{4 a x + 8 x}{3 x - 1} \div \frac{a + 2}{6 x - 2}
$$

**Step 1: Simplify the expression**
$$
= \frac{(4 a + 8)x}{3 x - 1} \cdot \frac{6 x - 2}{a + 2}
$$
Factoring out common terms:
$$
= \frac{(4a + 8)x(6x - 2)}{(3x - 1)(a + 2)}
$$
This simplifies to:
$$
= 8x
$$

**Step 2: Substitute values $$ x=-1 $$ and $$ a=2 $$**
$$
8 \cdot (-1) = -8
$$

### Problem 7
We need to simplify the expression:
$$
\frac{36 m^{2} n^{3}}{8 m} \div \frac{n^{2} m^{2}}{4 m n^{3}}
$$

**Step 1: Simplify the expression**
$$
= \frac{36 m^{2} n^{3}}{8 m} \cdot \frac{4 m n^{3}}{n^{2} m^{2}} = \frac{36 \cdot 4 n^{3}}{8 n^{2}} = \frac{144 n^{3}}{8 n^{2}} = 18 n^{4}
$$

**Step 2: Substitute values $$ m=3 $$ and $$ n=\frac{1}{3} $$**
$$
18 \left(\frac{1}{3}\right)^{4} = 18 \cdot \frac{1}{81} = \frac{2}{9}
$$

### Problem 8
We need to simplify the expression:
$$
\frac{3 x^{2} + 6 x}{2 x y + 4 y} \times \frac{2 y}{9 x^{2}}
$$

**Step 1: Simplify the expression**
$$
= \frac{3x(x + 2)}{2y(x + 2)} \cdot \frac{2y}{9x^{2}} = \frac{3x \cdot 2y}{2y \cdot 9x^{2}} = \frac{1}{3x}
$$

**Step 2: Substitute values $$ x=1 $$ and $$ y=2 $$**
$$
\frac{1}{3 \cdot 1} = \frac{1}{3}
$$

### Summary of Results
1. Problem 5: $$\frac{4}{7}$$
2. Problem 6: $$-8$$
3. Problem 7: $$\frac{2}{9}$$
4. Problem 8: $$\frac{1}{3}$$
1. Problem 5: $$ \frac{4}{7} $$ 2. Problem 6: $$ -8 $$ 3. Problem 7: $$ \frac{2}{9} $$ 4. Problem 8: $$ \frac{1}{3} $$

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Algebra Questions