Algebra Examples

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

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Multiply $3$ by $3$ .

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

Step 3

Multiply $x^{9}$ by $x$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $x$ .

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

Step 3.2

Multiply $x$ by $x^{9}$ .

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $1$ and $9$ .

$x^{10} {(y^{3})}^{3} \cdot y^{2}$

Step 4

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

Tap for more steps...

Step 4.1

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

$x^{10} y^{3 \cdot 3} \cdot y^{2}$

Step 4.2

Multiply $3$ by $3$ .

$x^{10} y^{9} \cdot y^{2}$

Step 5

Multiply $y^{9}$ by $y^{2}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $y^{2}$ .

$x^{10} (y^{2} y^{9})$

Step 5.2

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

$x^{10} y^{2 + 9}$

Step 5.3

Add $2$ and $9$ .

$x^{10} y^{11}$