Algebra Examples

$72 x^{14} y^{8} z^{14} \div 27 x^{3} y^{12} z^{14}$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Rewrite the division as a fraction.

$\frac{72 x^{14} y^{8} z^{14}}{27} x^{3} y^{12} z^{14}$

Step 1.2

Cancel the common factor of $72$ and $27$ .

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Step 1.2.1

Factor $9$ out of $72 x^{14} y^{8} z^{14}$ .

$\frac{9 (8 x^{14} y^{8} z^{14})}{27} x^{3} y^{12} z^{14}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $9$ out of $27$ .

$\frac{9 (8 x^{14} y^{8} z^{14})}{9 (3)} x^{3} y^{12} z^{14}$

Step 1.2.2.2

Cancel the common factor.

$\frac{9 (8 x^{14} y^{8} z^{14})}{9 \cdot 3} x^{3} y^{12} z^{14}$

Step 1.2.2.3

Rewrite the expression.

$\frac{8 x^{14} y^{8} z^{14}}{3} x^{3} y^{12} z^{14}$

Step 1.3

Multiply $\frac{8 x^{14} y^{8} z^{14}}{3} x^{3}$ .

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Step 1.3.1

Combine $\frac{8 x^{14} y^{8} z^{14}}{3}$ and $x^{3}$ .

$\frac{8 x^{14} y^{8} z^{14} x^{3}}{3} y^{12} z^{14}$

Step 1.3.2

Multiply $x^{14}$ by $x^{3}$ by adding the exponents.

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Step 1.3.2.1

Move $x^{3}$ .

$\frac{8 (x^{3} x^{14}) y^{8} z^{14}}{3} y^{12} z^{14}$

Step 1.3.2.2

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

$\frac{8 x^{3 + 14} y^{8} z^{14}}{3} y^{12} z^{14}$

Step 1.3.2.3

Add $3$ and $14$ .

$\frac{8 x^{17} y^{8} z^{14}}{3} y^{12} z^{14}$

Step 1.4

Multiply $\frac{8 x^{17} y^{8} z^{14}}{3} y^{12}$ .

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Step 1.4.1

Combine $\frac{8 x^{17} y^{8} z^{14}}{3}$ and $y^{12}$ .

$\frac{8 x^{17} y^{8} z^{14} y^{12}}{3} z^{14}$

Step 1.4.2

Multiply $y^{8}$ by $y^{12}$ by adding the exponents.

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Step 1.4.2.1

Move $y^{12}$ .

$\frac{8 x^{17} (y^{12} y^{8}) z^{14}}{3} z^{14}$

Step 1.4.2.2

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

$\frac{8 x^{17} y^{12 + 8} z^{14}}{3} z^{14}$

Step 1.4.2.3

Add $12$ and $8$ .

$\frac{8 x^{17} y^{20} z^{14}}{3} z^{14}$

Step 1.5

Multiply $\frac{8 x^{17} y^{20} z^{14}}{3} z^{14}$ .

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Step 1.5.1

Combine $\frac{8 x^{17} y^{20} z^{14}}{3}$ and $z^{14}$ .

$\frac{8 x^{17} y^{20} z^{14} z^{14}}{3}$

Step 1.5.2

Multiply $z^{14}$ by $z^{14}$ by adding the exponents.

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Step 1.5.2.1

Move $z^{14}$ .

$\frac{8 x^{17} y^{20} (z^{14} z^{14})}{3}$

Step 1.5.2.2

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

$\frac{8 x^{17} y^{20} z^{14 + 14}}{3}$

Step 1.5.2.3

Add $14$ and $14$ .

$\frac{8 x^{17} y^{20} z^{28}}{3}$

Step 2

The largest exponent is the degree of the polynomial.

$65$