Trigonometry Examples

${(- 5 x^{5} y^{2})}^{2} {(3 x^{2} y^{3})}^{3}$

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 $- 5 x^{5} y^{2}$ .

${(- 5 x^{5})}^{2} {(y^{2})}^{2} {(3 x^{2} y^{3})}^{3}$

Step 1.2

Apply the product rule to $- 5 x^{5}$ .

${(- 5)}^{2} {(x^{5})}^{2} {(y^{2})}^{2} {(3 x^{2} y^{3})}^{3}$

Step 2

Raise $- 5$ to the power of $2$ .

$25 {(x^{5})}^{2} {(y^{2})}^{2} {(3 x^{2} y^{3})}^{3}$

Step 3

Multiply the exponents in ${(x^{5})}^{2}$ .

Tap for more steps...

Step 3.1

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

$25 x^{5 \cdot 2} {(y^{2})}^{2} {(3 x^{2} y^{3})}^{3}$

Step 3.2

Multiply $5$ by $2$ .

$25 x^{10} {(y^{2})}^{2} {(3 x^{2} y^{3})}^{3}$

Step 4

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

Tap for more steps...

Step 4.1

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

$25 x^{10} y^{2 \cdot 2} {(3 x^{2} y^{3})}^{3}$

Step 4.2

Multiply $2$ by $2$ .

$25 x^{10} y^{4} {(3 x^{2} y^{3})}^{3}$

Step 5

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

Tap for more steps...

Step 5.1

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

$25 x^{10} y^{4} ({(3 x^{2})}^{3} {(y^{3})}^{3})$

Step 5.2

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

$25 x^{10} y^{4} (3^{3} {(x^{2})}^{3} {(y^{3})}^{3})$

Step 6

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

$25 x^{10} y^{4} (27 {(x^{2})}^{3} {(y^{3})}^{3})$

Step 7

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

Tap for more steps...

Step 7.1

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

$25 x^{10} y^{4} (27 x^{2 \cdot 3} {(y^{3})}^{3})$

Step 7.2

Multiply $2$ by $3$ .

$25 x^{10} y^{4} (27 x^{6} {(y^{3})}^{3})$

Step 8

Multiply $x^{10}$ by $x^{6}$ by adding the exponents.

Tap for more steps...

Step 8.1

Move $x^{6}$ .

$25 (x^{6} x^{10}) y^{4} (27 {(y^{3})}^{3})$

Step 8.2

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

$25 x^{6 + 10} y^{4} (27 {(y^{3})}^{3})$

Step 8.3

Add $6$ and $10$ .

$25 x^{16} y^{4} (27 {(y^{3})}^{3})$

Step 9

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

Tap for more steps...

Step 9.1

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

$25 x^{16} y^{4} (27 y^{3 \cdot 3})$

Step 9.2

Multiply $3$ by $3$ .

$25 x^{16} y^{4} (27 y^{9})$

Step 10

Multiply $y^{4}$ by $y^{9}$ by adding the exponents.

Tap for more steps...

Step 10.1

Move $y^{9}$ .

$25 x^{16} (y^{9} y^{4}) \cdot 27$

Step 10.2

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

$25 x^{16} y^{9 + 4} \cdot 27$

Step 10.3

Add $9$ and $4$ .

$25 x^{16} y^{13} \cdot 27$

Step 11

Multiply $27$ by $25$ .

$675 x^{16} y^{13}$