Trigonometry Examples

\frac{3 x^{- 4} y^{5}}{{(2 x^{3} y^{- 7})}^{- 2}}

$\frac{3 x^{- 4} y^{5}}{{(2 x^{3} y^{- 7})}^{- 2}}$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Move

x^{- 4}

$x^{- 4}$ to the denominator using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{3 y^{5}}{{(2 x^{3} y^{- 7})}^{- 2} x^{4}}

$\frac{3 y^{5}}{{(2 x^{3} y^{- 7})}^{- 2} x^{4}}$

Step 1.2

Move

{(2 x^{3} y^{- 7})}^{- 2}

${(2 x^{3} y^{- 7})}^{- 2}$ to the numerator using the negative exponent rule

\frac{1}{b^{- n}} = b^{n}

$\frac{1}{b^{- n}} = b^{n}$ .

\frac{3 y^{5} {(2 x^{3} y^{- 7})}^{2}}{x^{4}}

$\frac{3 y^{5} {(2 x^{3} y^{- 7})}^{2}}{x^{4}}$

\frac{3 y^{5} {(2 x^{3} y^{- 7})}^{2}}{x^{4}}

$\frac{3 y^{5} {(2 x^{3} y^{- 7})}^{2}}{x^{4}}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Apply the product rule to

2 x^{3} y^{- 7}

$2 x^{3} y^{- 7}$ .

\frac{3 y^{5} {(2 x^{3})}^{2} {(y^{- 7})}^{2}}{x^{4}}

$\frac{3 y^{5} {(2 x^{3})}^{2} {(y^{- 7})}^{2}}{x^{4}}$

Step 2.2

Apply the product rule to

2 x^{3}

$2 x^{3}$ .

\frac{3 y^{5} (2^{2} {(x^{3})}^{2}) {(y^{- 7})}^{2}}{x^{4}}

$\frac{3 y^{5} (2^{2} {(x^{3})}^{2}) {(y^{- 7})}^{2}}{x^{4}}$

Step 2.3

Raise

2

$2$ to the power of

2

$2$ .

\frac{3 y^{5} (4 {(x^{3})}^{2}) {(y^{- 7})}^{2}}{x^{4}}

$\frac{3 y^{5} (4 {(x^{3})}^{2}) {(y^{- 7})}^{2}}{x^{4}}$

Step 2.4

Multiply the exponents in

{(x^{3})}^{2}

${(x^{3})}^{2}$ .

Tap for more steps...

Step 2.4.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{3 y^{5} (4 x^{3 \cdot 2}) {(y^{- 7})}^{2}}{x^{4}}

$\frac{3 y^{5} (4 x^{3 \cdot 2}) {(y^{- 7})}^{2}}{x^{4}}$

Step 2.4.2

Multiply

3

$3$ by

2

$2$ .

\frac{3 y^{5} (4 x^{6}) {(y^{- 7})}^{2}}{x^{4}}

$\frac{3 y^{5} (4 x^{6}) {(y^{- 7})}^{2}}{x^{4}}$

\frac{3 y^{5} (4 x^{6}) {(y^{- 7})}^{2}}{x^{4}}

$\frac{3 y^{5} (4 x^{6}) {(y^{- 7})}^{2}}{x^{4}}$

Step 2.5

Multiply the exponents in

{(y^{- 7})}^{2}

${(y^{- 7})}^{2}$ .

Tap for more steps...

Step 2.5.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{3 y^{5} (4 x^{6}) y^{- 7 \cdot 2}}{x^{4}}

$\frac{3 y^{5} (4 x^{6}) y^{- 7 \cdot 2}}{x^{4}}$

Step 2.5.2

Multiply

- 7

$- 7$ by

2

$2$ .

\frac{3 y^{5} (4 x^{6}) y^{- 14}}{x^{4}}

$\frac{3 y^{5} (4 x^{6}) y^{- 14}}{x^{4}}$

\frac{3 y^{5} (4 x^{6}) y^{- 14}}{x^{4}}

$\frac{3 y^{5} (4 x^{6}) y^{- 14}}{x^{4}}$

Step 2.6

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{3 y^{5} \cdot 4 x^{6} \frac{1}{y^{14}}}{x^{4}}

$\frac{3 y^{5} \cdot 4 x^{6} \frac{1}{y^{14}}}{x^{4}}$

Step 2.7

Combine exponents.

Tap for more steps...

Step 2.7.1

Multiply

4

$4$ by

3

$3$ .

\frac{12 y^{5} x^{6} \frac{1}{y^{14}}}{x^{4}}

$\frac{12 y^{5} x^{6} \frac{1}{y^{14}}}{x^{4}}$

Step 2.7.2

Combine

12

$12$ and

\frac{1}{y^{14}}

$\frac{1}{y^{14}}$ .

\frac{y^{5} x^{6} \frac{12}{y^{14}}}{x^{4}}

$\frac{y^{5} x^{6} \frac{12}{y^{14}}}{x^{4}}$

Step 2.7.3

Combine

y^{5}

$y^{5}$ and

\frac{12}{y^{14}}

$\frac{12}{y^{14}}$ .

\frac{x^{6} \frac{y^{5} \cdot 12}{y^{14}}}{x^{4}}

$\frac{x^{6} \frac{y^{5} \cdot 12}{y^{14}}}{x^{4}}$

Step 2.7.4

Combine

x^{6}

$x^{6}$ and

\frac{y^{5} \cdot 12}{y^{14}}

$\frac{y^{5} \cdot 12}{y^{14}}$ .

\frac{\frac{x^{6} (y^{5} \cdot 12)}{y^{14}}}{x^{4}}

$\frac{\frac{x^{6} (y^{5} \cdot 12)}{y^{14}}}{x^{4}}$

\frac{\frac{x^{6} (y^{5} \cdot 12)}{y^{14}}}{x^{4}}

$\frac{\frac{x^{6} (y^{5} \cdot 12)}{y^{14}}}{x^{4}}$

Step 2.8

Remove unnecessary parentheses.

\frac{\frac{x^{6} y^{5} \cdot 12}{y^{14}}}{x^{4}}

$\frac{\frac{x^{6} y^{5} \cdot 12}{y^{14}}}{x^{4}}$

Step 2.9

Reduce the expression

\frac{x^{6} y^{5} \cdot 12}{y^{14}}

$\frac{x^{6} y^{5} \cdot 12}{y^{14}}$ by cancelling the common factors.

Tap for more steps...

Step 2.9.1

Factor

y^{5}

$y^{5}$ out of

x^{6} y^{5} \cdot 12

$x^{6} y^{5} \cdot 12$ .

\frac{\frac{y^{5} (x^{6} \cdot 12)}{y^{14}}}{x^{4}}

$\frac{\frac{y^{5} (x^{6} \cdot 12)}{y^{14}}}{x^{4}}$

Step 2.9.2

Factor

y^{5}

$y^{5}$ out of

y^{14}

$y^{14}$ .

\frac{\frac{y^{5} (x^{6} \cdot 12)}{y^{5} y^{9}}}{x^{4}}

$\frac{\frac{y^{5} (x^{6} \cdot 12)}{y^{5} y^{9}}}{x^{4}}$

Step 2.9.3

Cancel the common factor.

$\frac{\frac{y^{5} (x^{6} \cdot 12)}{y^{5} y^{9}}}{x^{4}}$

Step 2.9.4

Rewrite the expression.

$\frac{\frac{x^{6} \cdot 12}{y^{9}}}{x^{4}}$

Step 2.10

Move

$12$ to the left of

$x^{6}$ .

$\frac{\frac{12 x^{6}}{y^{9}}}{x^{4}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{12 x^{6}}{y^{9}} \cdot \frac{1}{x^{4}}$

Step 4

Combine.

$\frac{12 x^{6} \cdot 1}{y^{9} x^{4}}$

Step 5

Cancel the common factor of

$x^{6}$ and

$x^{4}$ .

Tap for more steps...

Step 5.1

Factor

$x^{4}$ out of

$12 x^{6} \cdot 1$ .

$\frac{x^{4} (12 x^{2} \cdot 1)}{y^{9} x^{4}}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor

$x^{4}$ out of

$y^{9} x^{4}$ .

$\frac{x^{4} (12 x^{2} \cdot 1)}{x^{4} y^{9}}$

Step 5.2.2

Cancel the common factor.

$\frac{x^{4} (12 x^{2} \cdot 1)}{x^{4} y^{9}}$

Step 5.2.3

Rewrite the expression.

$\frac{12 x^{2} \cdot 1}{y^{9}}$

Step 6

Multiply

$12$ by

$1$ .

$\frac{12 x^{2}}{y^{9}}$