Basic Math Examples

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

Step 1

Multiply ${(y^{3})}^{4}$ by ${(y^{3})}^{2}$ by adding the exponents.

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Step 1.1

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

$\frac{{(y^{3})}^{4 + 2}}{{(y^{2})}^{3}}$

Step 1.2

Add $4$ and $2$ .

$\frac{{(y^{3})}^{6}}{{(y^{2})}^{3}}$

Step 2

Apply basic rules of exponents.

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Step 2.1

Multiply the exponents in ${(y^{3})}^{6}$ .

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Step 2.1.1

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

$\frac{y^{3 \cdot 6}}{{(y^{2})}^{3}}$

Step 2.1.2

Multiply $3$ by $6$ .

$\frac{y^{18}}{{(y^{2})}^{3}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{y^{18}}{y^{2 \cdot 3}}$

Step 2.2.2

Multiply $2$ by $3$ .

$\frac{y^{18}}{y^{6}}$

Step 3

Cancel the common factor of $y^{18}$ and $y^{6}$ .

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Step 3.1

Factor $y^{6}$ out of $y^{18}$ .

$\frac{y^{6} y^{12}}{y^{6}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{y^{6} y^{12}}{y^{6} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{y^{6} y^{12}}{y^{6} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{y^{12}}{1}$

Step 3.2.4

Divide $y^{12}$ by $1$ .

$y^{12}$