Basic Math Examples

$\frac{y z^{2}}{{(2 z^{8} y^{10})}^{7} \cdot (2 z^{8})}$

Step 1

Cancel the common factor of $z^{2}$ and $z^{8}$ .

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Step 1.1

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

$\frac{z^{2} y}{{(2 z^{8} y^{10})}^{7} \cdot (2 z^{8})}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $z^{2}$ out of ${(2 z^{8} y^{10})}^{7} \cdot (2 z^{8})$ .

$\frac{z^{2} y}{z^{2} ({(2 z^{8} y^{10})}^{7} \cdot (2 z^{6}))}$

Step 1.2.2

Cancel the common factor.

$\frac{z^{2} y}{z^{2} ({(2 z^{8} y^{10})}^{7} \cdot (2 z^{6}))}$

Step 1.2.3

Rewrite the expression.

$\frac{y}{{(2 z^{8} y^{10})}^{7} \cdot (2 z^{6})}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2 z^{8} y^{10}$ .

$\frac{y}{{(2 z^{8})}^{7} {(y^{10})}^{7} \cdot 2 z^{6}}$

Step 2.2

Apply the product rule to $2 z^{8}$ .

$\frac{y}{2^{7} {(z^{8})}^{7} {(y^{10})}^{7} \cdot 2 z^{6}}$

Step 2.3

Raise $2$ to the power of $7$ .

$\frac{y}{128 {(z^{8})}^{7} {(y^{10})}^{7} \cdot 2 z^{6}}$

Step 2.4

Multiply the exponents in ${(z^{8})}^{7}$ .

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Step 2.4.1

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

$\frac{y}{128 z^{8 \cdot 7} {(y^{10})}^{7} \cdot 2 z^{6}}$

Step 2.4.2

Multiply $8$ by $7$ .

$\frac{y}{128 z^{56} {(y^{10})}^{7} \cdot 2 z^{6}}$

Step 2.5

Multiply the exponents in ${(y^{10})}^{7}$ .

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Step 2.5.1

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

$\frac{y}{128 z^{56} y^{10 \cdot 7} \cdot 2 z^{6}}$

Step 2.5.2

Multiply $10$ by $7$ .

$\frac{y}{128 z^{56} y^{70} \cdot 2 z^{6}}$

Step 2.6

Combine exponents.

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Step 2.6.1

Multiply $2$ by $128$ .

$\frac{y}{256 z^{56} y^{70} z^{6}}$

Step 2.6.2

Multiply $z^{56}$ by $z^{6}$ by adding the exponents.

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Step 2.6.2.1

Move $z^{6}$ .

$\frac{y}{256 (z^{6} z^{56}) y^{70}}$

Step 2.6.2.2

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

$\frac{y}{256 z^{6 + 56} y^{70}}$

Step 2.6.2.3

Add $6$ and $56$ .

$\frac{y}{256 z^{62} y^{70}}$

Step 3

Cancel the common factor of $y$ and $y^{70}$ .

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Step 3.1

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

$\frac{y^{1}}{256 z^{62} y^{70}}$

Step 3.2

Factor $y$ out of $y^{1}$ .

$\frac{y \cdot 1}{256 z^{62} y^{70}}$

Step 3.3

Cancel the common factors.

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Step 3.3.1

Factor $y$ out of $256 z^{62} y^{70}$ .

$\frac{y \cdot 1}{y (256 z^{62} y^{69})}$

Step 3.3.2

Cancel the common factor.

$\frac{y \cdot 1}{y (256 z^{62} y^{69})}$

Step 3.3.3

Rewrite the expression.

$\frac{1}{256 z^{62} y^{69}}$