Solved on Oct 20, 2023

Simplify the expression $\frac{6x^2}{60x^3}$ .

STEP 1

Assumptions1. The given expression is $\frac{6 x^{}}{60 x^{3}}$ . We are asked to simplify this expression

STEP 2

First, we can simplify the numerical part of the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is6.
$\frac{6 x^{2}}{60 x^{}} = \frac{6/6 x^{2}}{60/6 x^{}}$

STEP 3

Calculate the numerical part of the fraction.
$\frac{6/6 x^{2}}{60/6 x^{3}} = \frac{1 x^{2}}{10 x^{3}}$

STEP 4

Now, we can simplify the variable part of the fraction by subtracting the exponent of $x$ in the numerator from the exponent of $x$ in the denominator. This is based on the rule $x^{m}/x^{n} = x^{m-n}$ .
$\frac{1 x^{2}}{10 x^{3}} = \frac{1}{10} x^{2-3}$

STEP 5

Calculate the exponent of $x$ .
$\frac{1}{10} x^{2-3} = \frac{1}{10} x^{-1}$

STEP 6

Finally, we can rewrite $x^{-1}$ as $\frac{1}{x}$ to get rid of the negative exponent. This is based on the rule $x^{-n} =1/x^{n}$ .
$\frac{1}{10} x^{-1} = \frac{1}{10} \cdot \frac{1}{x}$

STEP 7

Calculate the final simplified form of the expression.
$\frac{1}{10} \cdot \frac{1}{x} = \frac{1}{10x}$ So, the simplest form of $\frac{6 x^{2}}{60 x^{3}}$ is $\frac{1}{10x}$ .

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Simplify the expression $\frac{6x^2}{60x^3}$ .

STEP 1

Assumptions1. The given expression is $\frac{6 x^{}}{60 x^{3}}$ . We are asked to simplify this expression

STEP 2

First, we can simplify the numerical part of the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is6.
$\frac{6 x^{2}}{60 x^{}} = \frac{6/6 x^{2}}{60/6 x^{}}$

STEP 3

Calculate the numerical part of the fraction.
$\frac{6/6 x^{2}}{60/6 x^{3}} = \frac{1 x^{2}}{10 x^{3}}$

STEP 4

Now, we can simplify the variable part of the fraction by subtracting the exponent of $x$ in the numerator from the exponent of $x$ in the denominator. This is based on the rule $x^{m}/x^{n} = x^{m-n}$ .
$\frac{1 x^{2}}{10 x^{3}} = \frac{1}{10} x^{2-3}$

STEP 5

Calculate the exponent of $x$ .
$\frac{1}{10} x^{2-3} = \frac{1}{10} x^{-1}$

STEP 6

Finally, we can rewrite $x^{-1}$ as $\frac{1}{x}$ to get rid of the negative exponent. This is based on the rule $x^{-n} =1/x^{n}$ .
$\frac{1}{10} x^{-1} = \frac{1}{10} \cdot \frac{1}{x}$

STEP 7

Calculate the final simplified form of the expression.
$\frac{1}{10} \cdot \frac{1}{x} = \frac{1}{10x}$ So, the simplest form of $\frac{6 x^{2}}{60 x^{3}}$ is $\frac{1}{10x}$ .

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Simplify the expression 6x260x3\frac{6x^2}{60x^3}60x36x2​.

STEP 1

Assumptions1. The given expression is 6x60x3\frac{6 x^{}}{60 x^{3}}60x36x​ . We are asked to simplify this expression

STEP 2

First, we can simplify the numerical part of the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is6.6x260x=6/6x260/6x\frac{6 x^{2}}{60 x^{}} = \frac{6/6 x^{2}}{60/6 x^{}}60x6x2​=60/6x6/6x2​

STEP 3

Calculate the numerical part of the fraction.6/6x260/6x3=1x210x3\frac{6/6 x^{2}}{60/6 x^{3}} = \frac{1 x^{2}}{10 x^{3}}60/6x36/6x2​=10x31x2​

STEP 4

STEP 5

Calculate the exponent of xxx.110x2−3=110x−1\frac{1}{10} x^{2-3} = \frac{1}{10} x^{-1}101​x2−3=101​x−1

STEP 6

Finally, we can rewrite x−1x^{-1}x−1 as 1x\frac{1}{x}x1​ to get rid of the negative exponent. This is based on the rule x−n=1/xnx^{-n} =1/x^{n}x−n=1/xn.110x−1=110⋅1x\frac{1}{10} x^{-1} = \frac{1}{10} \cdot \frac{1}{x}101​x−1=101​⋅x1​

STEP 7

Calculate the final simplified form of the expression.110⋅1x=110x\frac{1}{10} \cdot \frac{1}{x} = \frac{1}{10x}101​⋅x1​=10x1​So, the simplest form of 6x260x3\frac{6 x^{2}}{60 x^{3}}60x36x2​ is 110x\frac{1}{10x}10x1​.

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Simplify the expression $\frac{6x^2}{60x^3}$ .

Assumptions1. The given expression is $\frac{6 x^{}}{60 x^{3}}$ . We are asked to simplify this expression

First, we can simplify the numerical part of the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is6.
$\frac{6 x^{2}}{60 x^{}} = \frac{6/6 x^{2}}{60/6 x^{}}$

Calculate the numerical part of the fraction.
$\frac{6/6 x^{2}}{60/6 x^{3}} = \frac{1 x^{2}}{10 x^{3}}$

Calculate the exponent of $x$ .
$\frac{1}{10} x^{2-3} = \frac{1}{10} x^{-1}$

Finally, we can rewrite $x^{-1}$ as $\frac{1}{x}$ to get rid of the negative exponent. This is based on the rule $x^{-n} =1/x^{n}$ .
$\frac{1}{10} x^{-1} = \frac{1}{10} \cdot \frac{1}{x}$

Calculate the final simplified form of the expression.
$\frac{1}{10} \cdot \frac{1}{x} = \frac{1}{10x}$ So, the simplest form of $\frac{6 x^{2}}{60 x^{3}}$ is $\frac{1}{10x}$ .