Trigonometry Examples

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

Step 1

Simplify.

Tap for more steps...

Step 1.1

Move $x^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 1.2

Move ${(2 x^{3} y^{- 7})}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Apply the product rule to $2 x^{3} y^{- 7}$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

Tap for more steps...

Step 2.4.1

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

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

Step 2.4.2

Multiply $3$ by $2$ .

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

Step 2.5

Multiply the exponents in ${(y^{- 7})}^{2}$ .

Tap for more steps...

Step 2.5.1

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

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

Step 2.5.2

Multiply $- 7$ by $2$ .

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

Step 2.6

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2.7

Combine exponents.

Tap for more steps...

Step 2.7.1

Multiply $4$ by $3$ .

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

Step 2.7.2

Combine $12$ and $\frac{1}{y^{14}}$ .

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

Step 2.7.3

Combine $y^{5}$ and $\frac{12}{y^{14}}$ .

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

Step 2.7.4

Combine $x^{6}$ and $\frac{y^{5} \cdot 12}{y^{14}}$ .

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

Step 2.8

Remove unnecessary parentheses.

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

Step 2.9

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

Tap for more steps...

Step 2.9.1

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

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

Step 2.9.2

Factor $y^{5}$ out of $y^{14}$ .

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

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 $1$ .

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