Solve (2/k^3 5k^2-(1/k^2 5k))k^3 5k^2

Question

Simplify the expression

25 k^{4}

Evaluate

(\frac{2}{k ^{3}} \times 5 k^{2} - (\frac{1}{k ^{2}} \times 5 k)) k^{3} \times 5 k^{2}

Multiply the terms

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Multiply the terms

\frac{1}{k ^{2}} \times 5 k

Multiply the terms

\frac{5}{k ^{2}} \times k

Cancel out the common factor k

\frac{5}{k} \times 1

Multiply the terms

\frac{5}{k}

(\frac{2}{k ^{3}} \times 5 k^{2} - \frac{5}{k}) k^{3} \times 5 k^{2}

Multiply the terms

More Steps

Multiply the terms

\frac{2}{k ^{3}} \times 5 k^{2}

Multiply the terms

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Multiply the terms

\frac{2}{k ^{3}} \times 5

Multiply the terms

\frac{2 \times 5}{k ^{3}}

Multiply the terms

\frac{10}{k ^{3}}

\frac{10}{k ^{3}} \times k^{2}

Cancel out the common factor k^{2}

\frac{10}{k} \times 1

Multiply the terms

\frac{10}{k}

(\frac{10}{k} - \frac{5}{k}) k^{3} \times 5 k^{2}

Subtract the terms

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Simplify

\frac{10}{k} - \frac{5}{k}

Write all numerators above the common denominator

\frac{10 - 5}{k}

Subtract the numbers

\frac{5}{k}

\frac{5}{k} \times k^{3} \times 5 k^{2}

Multiply the terms with the same base by adding their exponents

\frac{5}{k} \times k^{3 + 2} \times 5

Add the numbers

\frac{5}{k} \times k^{5} \times 5

Cancel out the common factor k

5 k^{4} \times 5

Solution

25 k^{4}

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Find the excluded values

k = 0

Evaluate

(\frac{2}{k ^{3}} \times 5 k^{2} - (\frac{1}{k ^{2}} \times 5 k)) k^{3} \times 5 k^{2}

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

k^{3} = 0 k^{2} = 0

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

k = 0 k^{2} = 0

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

k = 0 k = 0

Solution

k = 0

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Find the roots

k \in \emptyset

Evaluate

(\frac{2}{k ^{3}} \times 5 k^{2} - (\frac{1}{k ^{2}} \times 5 k)) k^{3} \times 5 k^{2}

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

(\frac{2}{k ^{3}} \times 5 k^{2} - (\frac{1}{k ^{2}} \times 5 k)) k^{3} \times 5 k^{2} = 0

Find the domain

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Evaluate

{k^{3} \neq = 0 k^{2} \neq = 0

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

{k \neq = 0 k^{2} \neq = 0

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

{k \neq = 0 k \neq = 0

Find the intersection

k \neq = 0

(\frac{2}{k ^{3}} \times 5 k^{2} - (\frac{1}{k ^{2}} \times 5 k)) k^{3} \times 5 k^{2} = 0, k \neq = 0

Calculate

(\frac{2}{k ^{3}} \times 5 k^{2} - (\frac{1}{k ^{2}} \times 5 k)) k^{3} \times 5 k^{2} = 0

Multiply the terms

More Steps

Multiply the terms

\frac{1}{k ^{2}} \times 5 k

Multiply the terms

\frac{5}{k ^{2}} \times k

Cancel out the common factor k

\frac{5}{k} \times 1

Multiply the terms

\frac{5}{k}

(\frac{2}{k ^{3}} \times 5 k^{2} - \frac{5}{k}) k^{3} \times 5 k^{2} = 0

Multiply the terms

More Steps

Multiply the terms

\frac{2}{k ^{3}} \times 5 k^{2}

Multiply the terms

More Steps

Multiply the terms

\frac{2}{k ^{3}} \times 5

Multiply the terms

\frac{2 \times 5}{k ^{3}}

Multiply the terms

\frac{10}{k ^{3}}

\frac{10}{k ^{3}} \times k^{2}

Cancel out the common factor k^{2}

\frac{10}{k} \times 1

Multiply the terms

\frac{10}{k}

(\frac{10}{k} - \frac{5}{k}) k^{3} \times 5 k^{2} = 0

Subtract the terms

More Steps

Simplify

\frac{10}{k} - \frac{5}{k}

Write all numerators above the common denominator

\frac{10 - 5}{k}

Subtract the numbers

\frac{5}{k}

\frac{5}{k} \times k^{3} \times 5 k^{2} = 0

Multiply

More Steps

Multiply the terms

\frac{5}{k} \times k^{3} \times 5 k^{2}

Multiply the terms with the same base by adding their exponents

\frac{5}{k} \times k^{3 + 2} \times 5

Add the numbers

\frac{5}{k} \times k^{5} \times 5

Cancel out the common factor k

5 k^{4} \times 5

Multiply the numbers

25 k^{4}

25 k^{4} = 0

Rewrite the expression

k^{4} = 0

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

k = 0

Check if the solution is in the defined range

k = 0, k \neq = 0

Solution

k \in \emptyset

Show Solution