Basic Math Examples

$- 2 y z {(y^{2} z)}^{3} - 5 y^{5} {(y z^{2})}^{2}$

Step 1

Simplify each term.

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Step 1.1

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

$- 2 y z ({(y^{2})}^{3} z^{3}) - 5 y^{5} {(y z^{2})}^{2}$

Step 1.2

Multiply $z$ by $z^{3}$ by adding the exponents.

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Step 1.2.1

Move $z^{3}$ .

$- 2 y (z^{3} z) {(y^{2})}^{3} - 5 y^{5} {(y z^{2})}^{2}$

Step 1.2.2

Multiply $z^{3}$ by $z$ .

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Step 1.2.2.1

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

$- 2 y (z^{3} z^{1}) {(y^{2})}^{3} - 5 y^{5} {(y z^{2})}^{2}$

Step 1.2.2.2

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

$- 2 y z^{3 + 1} {(y^{2})}^{3} - 5 y^{5} {(y z^{2})}^{2}$

Step 1.2.3

Add $3$ and $1$ .

$- 2 y z^{4} {(y^{2})}^{3} - 5 y^{5} {(y z^{2})}^{2}$

Step 1.3

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

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Step 1.3.1

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

$- 2 y z^{4} y^{2 \cdot 3} - 5 y^{5} {(y z^{2})}^{2}$

Step 1.3.2

Multiply $2$ by $3$ .

$- 2 y z^{4} y^{6} - 5 y^{5} {(y z^{2})}^{2}$

Step 1.4

Multiply $y$ by $y^{6}$ by adding the exponents.

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Step 1.4.1

Move $y^{6}$ .

$- 2 (y^{6} y) z^{4} - 5 y^{5} {(y z^{2})}^{2}$

Step 1.4.2

Multiply $y^{6}$ by $y$ .

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Step 1.4.2.1

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

$- 2 (y^{6} y^{1}) z^{4} - 5 y^{5} {(y z^{2})}^{2}$

Step 1.4.2.2

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

$- 2 y^{6 + 1} z^{4} - 5 y^{5} {(y z^{2})}^{2}$

Step 1.4.3

Add $6$ and $1$ .

$- 2 y^{7} z^{4} - 5 y^{5} {(y z^{2})}^{2}$

Step 1.5

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

$- 2 y^{7} z^{4} - 5 y^{5} (y^{2} {(z^{2})}^{2})$

Step 1.6

Multiply $y^{5}$ by $y^{2}$ by adding the exponents.

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Step 1.6.1

Move $y^{2}$ .

$- 2 y^{7} z^{4} - 5 (y^{2} y^{5}) {(z^{2})}^{2}$

Step 1.6.2

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

$- 2 y^{7} z^{4} - 5 y^{2 + 5} {(z^{2})}^{2}$

Step 1.6.3

Add $2$ and $5$ .

$- 2 y^{7} z^{4} - 5 y^{7} {(z^{2})}^{2}$

Step 1.7

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

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Step 1.7.1

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

$- 2 y^{7} z^{4} - 5 y^{7} z^{2 \cdot 2}$

Step 1.7.2

Multiply $2$ by $2$ .

$- 2 y^{7} z^{4} - 5 y^{7} z^{4}$

Step 2

Subtract $5 y^{7} z^{4}$ from $- 2 y^{7} z^{4}$ .

$- 7 y^{7} z^{4}$