Basic Math Examples

$\frac{{(3 y^{7} z^{7})}^{2}}{y^{9}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $3 y^{7} z^{7}$ .

$\frac{{(3 y^{7})}^{2} {(z^{7})}^{2}}{y^{9}}$

Step 1.2

Apply the product rule to $3 y^{7}$ .

$\frac{3^{2} {(y^{7})}^{2} {(z^{7})}^{2}}{y^{9}}$

Step 1.3

Raise $3$ to the power of $2$ .

$\frac{9 {(y^{7})}^{2} {(z^{7})}^{2}}{y^{9}}$

Step 1.4

Multiply the exponents in ${(y^{7})}^{2}$ .

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Step 1.4.1

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

$\frac{9 y^{7 \cdot 2} {(z^{7})}^{2}}{y^{9}}$

Step 1.4.2

Multiply $7$ by $2$ .

$\frac{9 y^{14} {(z^{7})}^{2}}{y^{9}}$

Step 1.5

Multiply the exponents in ${(z^{7})}^{2}$ .

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Step 1.5.1

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

$\frac{9 y^{14} z^{7 \cdot 2}}{y^{9}}$

Step 1.5.2

Multiply $7$ by $2$ .

$\frac{9 y^{14} z^{14}}{y^{9}}$

Step 2

Cancel the common factor of $y^{14}$ and $y^{9}$ .

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Step 2.1

Factor $y^{9}$ out of $9 y^{14} z^{14}$ .

$\frac{y^{9} (9 y^{5} z^{14})}{y^{9}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{y^{9} (9 y^{5} z^{14})}{y^{9} \cdot 1}$

Step 2.2.2

Cancel the common factor.

$\frac{y^{9} (9 y^{5} z^{14})}{y^{9} \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{9 y^{5} z^{14}}{1}$

Step 2.2.4

Divide $9 y^{5} z^{14}$ by $1$ .

$9 y^{5} z^{14}$