Basic Math Examples

$\frac{{(3 y^{3})}^{5}}{9 y^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{3^{5} {(y^{3})}^{5}}{9 y^{2}}$

Step 1.2

Raise $3$ to the power of $5$ .

$\frac{243 {(y^{3})}^{5}}{9 y^{2}}$

Step 1.3

Multiply the exponents in ${(y^{3})}^{5}$ .

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Step 1.3.1

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

$\frac{243 y^{3 \cdot 5}}{9 y^{2}}$

Step 1.3.2

Multiply $3$ by $5$ .

$\frac{243 y^{15}}{9 y^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $243$ and $9$ .

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Step 2.1.1

Factor $9$ out of $243 y^{15}$ .

$\frac{9 (27 y^{15})}{9 y^{2}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $9$ out of $9 y^{2}$ .

$\frac{9 (27 y^{15})}{9 (y^{2})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{9 (27 y^{15})}{9 y^{2}}$

Step 2.1.2.3

Rewrite the expression.

$\frac{27 y^{15}}{y^{2}}$

Step 2.2

Cancel the common factor of $y^{15}$ and $y^{2}$ .

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Step 2.2.1

Factor $y^{2}$ out of $27 y^{15}$ .

$\frac{y^{2} (27 y^{13})}{y^{2}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Multiply by $1$ .

$\frac{y^{2} (27 y^{13})}{y^{2} \cdot 1}$

Step 2.2.2.2

Cancel the common factor.

$\frac{y^{2} (27 y^{13})}{y^{2} \cdot 1}$

Step 2.2.2.3

Rewrite the expression.

$\frac{27 y^{13}}{1}$

Step 2.2.2.4

Divide $27 y^{13}$ by $1$ .

$27 y^{13}$