Finite Math Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Apply the product rule to $- 3 x^{3} y^{3} z^{4}$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

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

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Multiply $3$ by $2$ .

$9 x^{6} {(y^{3})}^{2} {(z^{4})}^{2} {(2 y^{2})}^{3}$

Step 4

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

Tap for more steps...

Step 4.1

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

$9 x^{6} y^{3 \cdot 2} {(z^{4})}^{2} {(2 y^{2})}^{3}$

Step 4.2

Multiply $3$ by $2$ .

$9 x^{6} y^{6} {(z^{4})}^{2} {(2 y^{2})}^{3}$

Step 5

Multiply the exponents in ${(z^{4})}^{2}$ .

Tap for more steps...

Step 5.1

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

$9 x^{6} y^{6} z^{4 \cdot 2} {(2 y^{2})}^{3}$

Step 5.2

Multiply $4$ by $2$ .

$9 x^{6} y^{6} z^{8} {(2 y^{2})}^{3}$

Step 6

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

$9 x^{6} y^{6} z^{8} (2^{3} {(y^{2})}^{3})$

Step 7

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

$9 x^{6} y^{6} z^{8} (8 {(y^{2})}^{3})$

Step 8

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

Tap for more steps...

Step 8.1

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

$9 x^{6} y^{6} z^{8} (8 y^{2 \cdot 3})$

Step 8.2

Multiply $2$ by $3$ .

$9 x^{6} y^{6} z^{8} (8 y^{6})$

Step 9

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

Tap for more steps...

Step 9.1

Move $y^{6}$ .

$9 x^{6} (y^{6} y^{6}) z^{8} \cdot 8$

Step 9.2

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

$9 x^{6} y^{6 + 6} z^{8} \cdot 8$

Step 9.3

Add $6$ and $6$ .

$9 x^{6} y^{12} z^{8} \cdot 8$

Step 10

Multiply $8$ by $9$ .

$72 x^{6} y^{12} z^{8}$