Solve \dfrac{4}{3x^2 15x} \dfrac{7x}{x^2 10x^25}

Question

Simplify the expression

\frac{14}{1125 x ^{6}}

Evaluate

\frac{4}{3 x ^{2} \times 15 x} \times \frac{7 x}{x ^{2} \times 10 x ^{2} \times 5}

Reduce the fraction

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Evaluate

\frac{7 x}{x ^{2} \times 10 x ^{2} \times 5}

Multiply

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Evaluate

x^{2} \times 10 x^{2} \times 5

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 10 \times 5

Add the numbers

x^{4} \times 10 \times 5

Multiply the terms

x^{4} \times 50

\frac{7 x}{x ^{4} \times 50}

Reduce the fraction

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Calculate

\frac{x}{x ^{4}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{x ^{4 - 1}}

Subtract the terms

\frac{1}{x ^{3}}

\frac{7}{x ^{3} \times 50}

Calculate

\frac{7}{50 x ^{3}}

\frac{4}{3 x ^{2} \times 15 x} \times \frac{7}{50 x ^{3}}

Multiply

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Multiply the terms

3 x^{2} \times 15 x

Multiply the terms

45 x^{2} \times x

Multiply the terms with the same base by adding their exponents

45 x^{2 + 1}

Add the numbers

45 x^{3}

\frac{4}{45 x ^{3}} \times \frac{7}{50 x ^{3}}

Cancel out the common factor 2

\frac{2}{45 x ^{3}} \times \frac{7}{25 x ^{3}}

Multiply the terms

\frac{2 \times 7}{45 x ^{3} \times 25 x ^{3}}

Multiply the terms

\frac{14}{45 x ^{3} \times 25 x ^{3}}

Solution

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Evaluate

45 x^{3} \times 25 x^{3}

Multiply the numbers

1125 x^{3} \times x^{3}

Multiply the terms

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Evaluate

x^{3} \times x^{3}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 3}

Add the numbers

x^{6}

1125 x^{6}

\frac{14}{1125 x ^{6}}

Show Solution

Find the excluded values

x = 0

Evaluate

\frac{4}{3 x ^{2} \times 15 x} \times \frac{7 x}{x ^{2} \times 10 x ^{2} \times 5}

To find the excluded values,set the denominators equal to 0

x^{2} \times x = 0 x^{2} \times x^{2} = 0

Solve the equations

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Evaluate

x^{2} \times x = 0

Multiply the terms

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Evaluate

x^{2} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 1}

Add the numbers

x^{3}

x^{3} = 0

The only way a power can be 0 is when the base equals 0

x = 0

x = 0 x^{2} \times x^{2} = 0

Solve the equations

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Evaluate

x^{2} \times x^{2} = 0

Multiply the terms

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Evaluate

x^{2} \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 2}

Add the numbers

x^{4}

x^{4} = 0

The only way a power can be 0 is when the base equals 0

x = 0

x = 0 x = 0

Solution

x = 0

Show Solution

Find the roots

x \in \emptyset

Evaluate

\frac{4}{3 x ^{2} \times 15 x} \times \frac{7 x}{x ^{2} \times 10 x ^{2} \times 5}

To find the roots of the expression,set the expression equal to 0

\frac{4}{3 x ^{2} \times 15 x} \times \frac{7 x}{x ^{2} \times 10 x ^{2} \times 5} = 0

Find the domain

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Evaluate

{x^{2} \times x \neq = 0 x^{2} \times x^{2} \neq = 0

Calculate

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Evaluate

x^{2} \times x \neq = 0

Multiply the terms

x^{3} \neq = 0

The only way a power can not be 0 is when the base not equals 0

x \neq = 0

{x \neq = 0 x^{2} \times x^{2} \neq = 0

Calculate

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Evaluate

x^{2} \times x^{2} \neq = 0

Multiply the terms

x^{4} \neq = 0

The only way a power can not be 0 is when the base not equals 0

x \neq = 0

{x \neq = 0 x \neq = 0

Find the intersection

x \neq = 0

\frac{4}{3 x ^{2} \times 15 x} \times \frac{7 x}{x ^{2} \times 10 x ^{2} \times 5} = 0, x \neq = 0

Calculate

\frac{4}{3 x ^{2} \times 15 x} \times \frac{7 x}{x ^{2} \times 10 x ^{2} \times 5} = 0

Multiply

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Multiply the terms

3 x^{2} \times 15 x

Multiply the terms

45 x^{2} \times x

Multiply the terms with the same base by adding their exponents

45 x^{2 + 1}

Add the numbers

45 x^{3}

\frac{4}{45 x ^{3}} \times \frac{7 x}{x ^{2} \times 10 x ^{2} \times 5} = 0

Multiply

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Multiply the terms

x^{2} \times 10 x^{2} \times 5

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 10 \times 5

Add the numbers

x^{4} \times 10 \times 5

Multiply the terms

x^{4} \times 50

Use the commutative property to reorder the terms

50 x^{4}

\frac{4}{45 x ^{3}} \times \frac{7 x}{50 x ^{4}} = 0

Divide the terms

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Evaluate

\frac{7 x}{50 x ^{4}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{7}{50 x ^{4 - 1}}

Reduce the fraction

\frac{7}{50 x ^{3}}

\frac{4}{45 x ^{3}} \times \frac{7}{50 x ^{3}} = 0

Multiply the terms

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Multiply the terms

\frac{4}{45 x ^{3}} \times \frac{7}{50 x ^{3}}

Cancel out the common factor 2

\frac{2}{45 x ^{3}} \times \frac{7}{25 x ^{3}}

Multiply the terms

\frac{2 \times 7}{45 x ^{3} \times 25 x ^{3}}

Multiply the terms

\frac{14}{45 x ^{3} \times 25 x ^{3}}

Multiply the terms

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Evaluate

45 x^{3} \times 25 x^{3}

Multiply the numbers

1125 x^{3} \times x^{3}

Multiply the terms

1125 x^{6}

\frac{14}{1125 x ^{6}}

\frac{14}{1125 x ^{6}} = 0

Cross multiply

14 = 1125 x^{6} \times 0

Simplify the equation

14 = 0

Solution

x \in \emptyset

Show Solution