Basic Math Examples

$\frac{- 5 t^{3} y^{4}}{t^{2} y^{- 1}} \cdot \frac{{(3 t^{2} y^{2})}^{3}}{t^{3} y}$

Step 1

Combine.

$\frac{- 5 t^{3} y^{4} {(3 t^{2} y^{2})}^{3}}{t^{2} y^{- 1} (t^{3} y)}$

Step 2

Multiply $t^{2}$ by $t^{3}$ by adding the exponents.

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Step 2.1

Move $t^{3}$ .

$\frac{- 5 t^{3} y^{4} {(3 t^{2} y^{2})}^{3}}{t^{3} t^{2} y^{- 1} y}$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 5 t^{3} y^{4} {(3 t^{2} y^{2})}^{3}}{t^{3 + 2} y^{- 1} y}$

Step 2.3

Add $3$ and $2$ .

$\frac{- 5 t^{3} y^{4} {(3 t^{2} y^{2})}^{3}}{t^{5} y^{- 1} y}$

Step 3

Multiply $y^{- 1}$ by $y$ by adding the exponents.

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Step 3.1

Move $y$ .

$\frac{- 5 t^{3} y^{4} {(3 t^{2} y^{2})}^{3}}{t^{5} (y \cdot y^{- 1})}$

Step 3.2

Multiply $y$ by $y^{- 1}$ .

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Step 3.2.1

Raise $y$ to the power of $1$ .

$\frac{- 5 t^{3} y^{4} {(3 t^{2} y^{2})}^{3}}{t^{5} (y^{1} y^{- 1})}$

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 5 t^{3} y^{4} {(3 t^{2} y^{2})}^{3}}{t^{5} y^{1 - 1}}$

Step 3.3

Subtract $1$ from $1$ .

$\frac{- 5 t^{3} y^{4} {(3 t^{2} y^{2})}^{3}}{t^{5} y^{0}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Simplify $t^{5} y^{0}$ .

$\frac{- 5 t^{3} y^{4} {(3 t^{2} y^{2})}^{3}}{t^{5}}$

Step 4.2

Cancel the common factor of $t^{3}$ and $t^{5}$ .

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Step 4.2.1

Factor $t^{3}$ out of $- 5 t^{3} y^{4} {(3 t^{2} y^{2})}^{3}$ .

$\frac{t^{3} (- 5 y^{4} {(3 t^{2} y^{2})}^{3})}{t^{5}}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $t^{3}$ out of $t^{5}$ .

$\frac{t^{3} (- 5 y^{4} {(3 t^{2} y^{2})}^{3})}{t^{3} t^{2}}$

Step 4.2.2.2

Cancel the common factor.

$\frac{t^{3} (- 5 y^{4} {(3 t^{2} y^{2})}^{3})}{t^{3} t^{2}}$

Step 4.2.2.3

Rewrite the expression.

$\frac{- 5 y^{4} {(3 t^{2} y^{2})}^{3}}{t^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the product rule to $3 t^{2} y^{2}$ .

$\frac{- 5 y^{4} {(3 t^{2})}^{3} {(y^{2})}^{3}}{t^{2}}$

Step 5.2

Apply the product rule to $3 t^{2}$ .

$\frac{- 5 y^{4} (3^{3} {(t^{2})}^{3}) {(y^{2})}^{3}}{t^{2}}$

Step 5.3

Raise $3$ to the power of $3$ .

$\frac{- 5 y^{4} (27 {(t^{2})}^{3}) {(y^{2})}^{3}}{t^{2}}$

Step 5.4

Multiply the exponents in ${(t^{2})}^{3}$ .

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Step 5.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- 5 y^{4} (27 t^{2 \cdot 3}) {(y^{2})}^{3}}{t^{2}}$

Step 5.4.2

Multiply $2$ by $3$ .

$\frac{- 5 y^{4} (27 t^{6}) {(y^{2})}^{3}}{t^{2}}$

Step 5.5

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 5.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- 5 y^{4} (27 t^{6}) y^{2 \cdot 3}}{t^{2}}$

Step 5.5.2

Multiply $2$ by $3$ .

$\frac{- 5 y^{4} (27 t^{6}) y^{6}}{t^{2}}$

$\frac{- 5 y^{4} \cdot 27 t^{6} y^{6}}{t^{2}}$

Step 5.6

Combine exponents.

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Step 5.6.1

Multiply $27$ by $- 5$ .

$\frac{- 135 y^{4} t^{6} y^{6}}{t^{2}}$

Step 5.6.2

Multiply $y^{4}$ by $y^{6}$ by adding the exponents.

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Step 5.6.2.1

Move $y^{6}$ .

$\frac{- 135 (y^{6} y^{4}) t^{6}}{t^{2}}$

Step 5.6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 135 y^{6 + 4} t^{6}}{t^{2}}$

Step 5.6.2.3

Add $6$ and $4$ .

$\frac{- 135 y^{10} t^{6}}{t^{2}}$

Step 6

Cancel the common factor of $t^{6}$ and $t^{2}$ .

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Step 6.1

Factor $t^{2}$ out of $- 135 y^{10} t^{6}$ .

$\frac{t^{2} (- 135 y^{10} t^{4})}{t^{2}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Multiply by $1$ .

$\frac{t^{2} (- 135 y^{10} t^{4})}{t^{2} \cdot 1}$

Step 6.2.2

Cancel the common factor.

$\frac{t^{2} (- 135 y^{10} t^{4})}{t^{2} \cdot 1}$

Step 6.2.3

Rewrite the expression.

$\frac{- 135 y^{10} t^{4}}{1}$

Step 6.2.4

Divide $- 135 y^{10} t^{4}$ by $1$ .

$- 135 y^{10} t^{4}$