Algebra Examples

$3 y^{3} z^{4} \cdot 3 x^{4} y^{2} z^{- 3} \cdot x^{- 2} y^{4} z^{2}$

Step 1

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

Tap for more steps...

Step 1.1

Move $y^{2}$ .

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

Step 1.2

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

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

Step 1.3

Add $2$ and $3$ .

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

Step 2

Multiply $y^{5}$ by $y^{4}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $y^{4}$ .

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

Step 2.2

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

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

Step 2.3

Add $4$ and $5$ .

$3 y^{9} z^{4} \cdot (3 x^{4} z^{- 3}) \cdot (x^{- 2} z^{2})$

Step 3

Multiply $z^{4}$ by $z^{- 3}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $z^{- 3}$ .

$3 y^{9} (z^{- 3} z^{4}) \cdot (3 x^{4}) \cdot (x^{- 2} z^{2})$

Step 3.2

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

$3 y^{9} z^{- 3 + 4} \cdot (3 x^{4}) \cdot (x^{- 2} z^{2})$

Step 3.3

Add $- 3$ and $4$ .

$3 y^{9} z^{1} \cdot (3 x^{4}) \cdot (x^{- 2} z^{2})$

Step 4

Simplify $3 y^{9} z^{1} \cdot (3 x^{4}) \cdot (x^{- 2} z^{2})$ .

$3 y^{9} z \cdot (3 x^{4}) \cdot (x^{- 2} z^{2})$

Step 5

Multiply $z$ by $z^{2}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $z^{2}$ .

$3 y^{9} (z^{2} z) \cdot (3 x^{4}) \cdot x^{- 2}$

Step 5.2

Multiply $z^{2}$ by $z$ .

Tap for more steps...

Step 5.2.1

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

$3 y^{9} (z^{2} z^{1}) \cdot (3 x^{4}) \cdot x^{- 2}$

Step 5.2.2

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

$3 y^{9} z^{2 + 1} \cdot (3 x^{4}) \cdot x^{- 2}$

Step 5.3

Add $2$ and $1$ .

$3 y^{9} z^{3} \cdot (3 x^{4}) \cdot x^{- 2}$

Step 6

Multiply $x^{4}$ by $x^{- 2}$ by adding the exponents.

Tap for more steps...

Step 6.1

Move $x^{- 2}$ .

$3 y^{9} z^{3} \cdot (3 (x^{- 2} x^{4}))$

Step 6.2

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

$3 y^{9} z^{3} \cdot (3 x^{- 2 + 4})$

Step 6.3

Add $- 2$ and $4$ .

$3 y^{9} z^{3} \cdot (3 x^{2})$

Step 7

Multiply $3$ by $3$ .

$9 y^{9} z^{3} x^{2}$