new: simplify. your answer should contain only positive exponents. simplificar. tu respuesta debe contener sólo exponentes positivos.
9) $\frac{u^2v^3}{4u^3v^3}$
10) $\frac{2x^3y^3}{yx^2}$
11) $\frac{3m^2n^2p^2}{m^3n^4p^3}$
12) $\frac{2a^3b^2c^4}{4ab^2c^4}$
13) $\frac{2pm^4n^2}{m^4n^4}$
14) $\frac{3x^4y^0z^4}{2x^2y^4}$
15) $\frac{3y^0z^3}{4yx^2z^4}$
16) $\frac{2zy^3}{3x^3y^3z^2}$

Question

Accepted Answer

### Problem 9: $\boldsymbol{\frac{u^2 v^3}{4u^3 v^3}}$
# Explanation:
## Step 1: Simplify $u$ terms
Use the exponent rule $\frac{a^m}{a^n}=a^{m - n}$. For $u$: $\frac{u^2}{u^3}=u^{2-3}=u^{-1}=\frac{1}{u}$ (but we'll keep it as $u^{-1}$ for now and handle later to ensure positive exponents).
## Step 2: Simplify $v$ terms
For $v$: $\frac{v^3}{v^3}=v^{3 - 3}=v^0 = 1$ (since any non - zero number to the power of 0 is 1).
## Step 3: Combine and simplify
The expression becomes $\frac{1	imes1}{4u^{1}	imes1}=\frac{1}{4u}$ (we converted $u^{-1}$ to $\frac{1}{u}$ to have positive exponents).
# Answer:
$\frac{1}{4u}$

### Problem 10: $\boldsymbol{\frac{2x^3 y^3}{y x^2}}$
# Explanation:
## Step 1: Simplify $x$ terms
Using $\frac{a^m}{a^n}=a^{m - n}$, for $x$: $\frac{x^3}{x^2}=x^{3-2}=x^1=x$.
## Step 2: Simplify $y$ terms
For $y$: $\frac{y^3}{y}=y^{3 - 1}=y^2$.
## Step 3: Multiply the coefficient and simplified terms
The coefficient is 2, so we have $2	imes x	imes y^2 = 2xy^2$.
# Answer:
$2xy^2$

### Problem 11: $\boldsymbol{\frac{3m^2 n^2 p^2}{m^3 n^4 p^3}}$
# Explanation:
## Step 1: Simplify $m$ terms
Using $\frac{a^m}{a^n}=a^{m - n}$, for $m$: $\frac{m^2}{m^3}=m^{2-3}=m^{-1}=\frac{1}{m}$.
## Step 2: Simplify $n$ terms
For $n$: $\frac{n^2}{n^4}=n^{2 - 4}=n^{-2}=\frac{1}{n^2}$.
## Step 3: Simplify $p$ terms
For $p$: $\frac{p^2}{p^3}=p^{2-3}=p^{-1}=\frac{1}{p}$.
## Step 4: Combine with the coefficient
The coefficient is 3, so we have $3	imes\frac{1}{m}	imes\frac{1}{n^2}	imes\frac{1}{p}=\frac{3}{m n^2 p}$.
# Answer:
$\frac{3}{m n^2 p}$

### Problem 12: $\boldsymbol{\frac{2a^3 b^2 c^4}{4ab^2 c^4}}$
# Explanation:
## Step 1: Simplify the coefficient
$\frac{2}{4}=\frac{1}{2}$.
## Step 2: Simplify $a$ terms
Using $\frac{a^m}{a^n}=a^{m - n}$, for $a$: $\frac{a^3}{a}=a^{3-1}=a^2$.
## Step 3: Simplify $b$ terms
For $b$: $\frac{b^2}{b^2}=b^{2 - 2}=b^0 = 1$.
## Step 4: Simplify $c$ terms
For $c$: $\frac{c^4}{c^4}=c^{4 - 4}=c^0 = 1$.
## Step 5: Combine the terms
We have $\frac{1}{2}	imes a^2	imes1	imes1=\frac{a^2}{2}$.
# Answer:
$\frac{a^2}{2}$

### Problem 13: $\boldsymbol{\frac{2p m^4 n^2}{m^4 n^4}}$
# Explanation:
## Step 1: Simplify $m$ terms
For $m$: $\frac{m^4}{m^4}=m^{4 - 4}=m^0 = 1$.
## Step 2: Simplify $n$ terms
Using $\frac{a^m}{a^n}=a^{m - n}$, for $n$: $\frac{n^2}{n^4}=n^{2-4}=n^{-2}=\frac{1}{n^2}$.
## Step 3: Combine with the coefficient and $p$
The coefficient is 2 and we have $p$ as it is. So we get $2	imes p	imes1	imes\frac{1}{n^2}=\frac{2p}{n^2}$.
# Answer:
$\frac{2p}{n^2}$

### Problem 14: $\boldsymbol{\frac{3x^4 y^0 z^4}{2x^2 y^4}}$
# Explanation:
## Step 1: Simplify $y$ term
Since $y^0 = 1$, the $y$ term in the numerator is 1.
## Step 2: Simplify $x$ terms
Using $\frac{a^m}{a^n}=a^{m - n}$, for $x$: $\frac{x^4}{x^2}=x^{4-2}=x^2$.
## Step 3: Simplify $z$ and $y$ terms
The $z$ term is $z^4$ (remains as it is for now) and the $y$ term in the denominator is $y^4$. So we have $\frac{3	imes x^2	imes1	imes z^4}{2	imes y^4}=\frac{3x^2 z^4}{2y^4}$.
# Answer:
$\frac{3x^2 z^4}{2y^4}$

### Problem 15: $\boldsymbol{\frac{3y^0 z^3}{4y x^2 z^4}}$
# Explanation:
## Step 1: Simplify $y$ terms
Since $y^0 = 1$, the numerator $y$ term is 1. For the $y$ terms: $\frac{1}{y}=y^{-1}=\frac{1}{y}$.
## Step 2: Simplify $z$ terms
Using $\frac{a^m}{a^n}=a^{m - n}$, for $z$: $\frac{z^3}{z^4}=z^{3-4}=z^{-1}=\frac{1}{z}$.
## Step 3: Combine with the coefficient and $x$ term
The coefficient is 3, the $x$ term is $x^2$ (in the denominator). So we get $\frac{3	imes1	imes1}{4	imes y	imes x^2	imes z}=\frac{3}{4x^2 y z}$.
# Answer:
$\frac{3}{4x^2 y z}$

### Problem 16: $\boldsymbol{\frac{2z y^3}{3x^3 y^3 z^2}}$
# Explanation:
## Step 1: Simplify $y$ terms
For $y$: $\frac{y^3}{y^3}=y^{3 - 3}=y^0 = 1$.
## Step 2: Simplify $z$ terms
Using $\frac{a^m}{a^n}=a^{m - n}$, for $z$: $\frac{z}{z^2}=z^{1-2}=z^{-1}=\frac{1}{z}$.
## Step 3: Simplify $x$ terms
The $x$ term is $x^3$ (in the denominator).
## Step 4: Combine with the coefficient
The coefficient is $\frac{2}{3}$, so we have $\frac{2	imes1	imes1}{3	imes x^3	imes1	imes z}=\frac{2}{3x^3 z}$.
# Answer:
$\frac{2}{3x^3 z}$

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QUESTION IMAGE

Question

Explanation:

Problem 9: $\boldsymbol{\frac{u^2 v^3}{4u^3 v^3}}$

Step 1: Simplify $u$ terms

Step 2: Simplify $v$ terms

Step 3: Combine and simplify

Step 1: Simplify $x$ terms

Step 2: Simplify $y$ terms

Step 3: Multiply the coefficient and simplified terms

Step 1: Simplify $m$ terms

Step 2: Simplify $n$ terms

Step 3: Simplify $p$ terms

Step 4: Combine with the coefficient

Answer:

Problem 10: $\boldsymbol{\frac{2x^3 y^3}{y x^2}}$