Basic Math Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 2.1

Apply the product rule to $- 3 s^{2} y^{3} z^{2}$ .

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

Step 2.2

Apply the product rule to $- 3 s^{2} y^{3}$ .

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

Step 2.3

Apply the product rule to $- 3 s^{2}$ .

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

Step 3

Raise $- 3$ to the power of $2$ .

$3 (9 {(s^{2})}^{2} {(y^{3})}^{2} {(z^{2})}^{2}) s^{2} y$

Step 4

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

Tap for more steps...

Step 4.1

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

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

Step 4.2

Multiply $2$ by $2$ .

$3 (9 s^{4} {(y^{3})}^{2} {(z^{2})}^{2}) s^{2} y$

Step 5

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

Tap for more steps...

Step 5.1

Move $s^{2}$ .

$3 (9 (s^{2} s^{4}) {(y^{3})}^{2} {(z^{2})}^{2}) y$

Step 5.2

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

$3 (9 s^{2 + 4} {(y^{3})}^{2} {(z^{2})}^{2}) y$

Step 5.3

Add $2$ and $4$ .

$3 (9 s^{6} {(y^{3})}^{2} {(z^{2})}^{2}) y$

Step 6

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

Tap for more steps...

Step 6.1

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

$3 (9 s^{6} y^{3 \cdot 2} {(z^{2})}^{2}) y$

Step 6.2

Multiply $3$ by $2$ .

$3 (9 s^{6} y^{6} {(z^{2})}^{2}) y$

Step 7

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

Tap for more steps...

Step 7.1

Move $y$ .

$3 (9 s^{6} (y \cdot y^{6}) {(z^{2})}^{2})$

Step 7.2

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

Tap for more steps...

Step 7.2.1

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

$3 (9 s^{6} (y^{1} y^{6}) {(z^{2})}^{2})$

Step 7.2.2

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

$3 (9 s^{6} y^{1 + 6} {(z^{2})}^{2})$

Step 7.3

Add $1$ and $6$ .

$3 (9 s^{6} y^{7} {(z^{2})}^{2})$

Step 8

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

Tap for more steps...

Step 8.1

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

$3 (9 s^{6} y^{7} z^{2 \cdot 2})$

Step 8.2

Multiply $2$ by $2$ .

$3 (9 s^{6} y^{7} z^{4})$

Step 9

Multiply $9$ by $3$ .

$27 s^{6} y^{7} z^{4}$