Finite Math Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

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 $- 2 x^{4} y^{2}$ .

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

Step 2.2

Apply the product rule to $- 2 x^{4}$ .

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

Step 3

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

$3 (- 8 {(x^{4})}^{3} {(y^{2})}^{3}) x^{3} y^{3} z$

Step 4

Multiply the exponents in ${(x^{4})}^{3}$ .

Tap for more steps...

Step 4.1

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

$3 (- 8 x^{4 \cdot 3} {(y^{2})}^{3}) x^{3} y^{3} z$

Step 4.2

Multiply $4$ by $3$ .

$3 (- 8 x^{12} {(y^{2})}^{3}) x^{3} y^{3} z$

Step 5

Multiply $x^{12}$ by $x^{3}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $x^{3}$ .

$3 (- 8 (x^{3} x^{12}) {(y^{2})}^{3}) y^{3} z$

Step 5.2

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

$3 (- 8 x^{3 + 12} {(y^{2})}^{3}) y^{3} z$

Step 5.3

Add $3$ and $12$ .

$3 (- 8 x^{15} {(y^{2})}^{3}) y^{3} z$

Step 6

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

Tap for more steps...

Step 6.1

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

$3 (- 8 x^{15} y^{2 \cdot 3}) y^{3} z$

Step 6.2

Multiply $2$ by $3$ .

$3 (- 8 x^{15} y^{6}) y^{3} z$

Step 7

Multiply $y^{6}$ by $y^{3}$ by adding the exponents.

Tap for more steps...

Step 7.1

Move $y^{3}$ .

$3 (- 8 x^{15} (y^{3} y^{6})) z$

Step 7.2

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

$3 (- 8 x^{15} y^{3 + 6}) z$

Step 7.3

Add $3$ and $6$ .

$3 (- 8 x^{15} y^{9}) z$

Step 8

Multiply $- 8$ by $3$ .

$- 24 x^{15} y^{9} z$