Trigonometry Examples

${(\frac{5 r^{2} s}{2 t^{3}})}^{- 1} (\frac{8 r s^{3}}{7 t^{2}})$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{2 t^{3}}{5 r^{2} s} \cdot \frac{8 r s^{3}}{7 t^{2}}$

Step 2

Combine.

$\frac{2 t^{3} (8 r s^{3})}{5 r^{2} s (7 t^{2})}$

Step 3

Cancel the common factor of $t^{3}$ and $t^{2}$ .

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Step 3.1

Factor $t^{2}$ out of $2 t^{3} (8 r s^{3})$ .

$\frac{t^{2} (2 t (8 r s^{3}))}{5 r^{2} s (7 t^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $t^{2}$ out of $5 r^{2} s (7 t^{2})$ .

$\frac{t^{2} (2 t (8 r s^{3}))}{t^{2} (5 r^{2} s \cdot (7))}$

Step 3.2.2

Cancel the common factor.

$\frac{t^{2} (2 t (8 r s^{3}))}{t^{2} (5 r^{2} s \cdot (7))}$

Step 3.2.3

Rewrite the expression.

$\frac{2 t (8 r s^{3})}{5 r^{2} s \cdot (7)}$

Step 4

Cancel the common factor of $r$ and $r^{2}$ .

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Step 4.1

Factor $r$ out of $2 t (8 r s^{3})$ .

$\frac{r (2 t (8 s^{3}))}{5 r^{2} s \cdot (7)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $r$ out of $5 r^{2} s \cdot (7)$ .

$\frac{r (2 t (8 s^{3}))}{r (5 r s \cdot 7)}$

Step 4.2.2

Cancel the common factor.

$\frac{r (2 t (8 s^{3}))}{r (5 r s \cdot 7)}$

Step 4.2.3

Rewrite the expression.

$\frac{2 t (8 s^{3})}{5 r s \cdot 7}$

Step 5

Cancel the common factor of $s^{3}$ and $s$ .

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Step 5.1

Factor $s$ out of $2 t (8 s^{3})$ .

$\frac{s (2 t (8 s^{2}))}{5 r s \cdot 7}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $s$ out of $5 r s \cdot 7$ .

$\frac{s (2 t (8 s^{2}))}{s (5 r \cdot 7)}$

Step 5.2.2

Cancel the common factor.

$\frac{s (2 t (8 s^{2}))}{s (5 r \cdot 7)}$

Step 5.2.3

Rewrite the expression.

$\frac{2 t (8 s^{2})}{5 r \cdot 7}$

Step 6

Multiply.

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Step 6.1

Multiply $8$ by $2$ .

$\frac{16 t s^{2}}{5 r \cdot 7}$

Step 6.2

Multiply $7$ by $5$ .

$\frac{16 t s^{2}}{35 r}$