Simplify (6/7)^-2*((4s)/(6t))^-2

${(\frac{6}{7})}^{- 2} \cdot {(\frac{4 s}{6 t})}^{- 2}$

Step 1

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

${(\frac{7}{6})}^{2} \cdot {(\frac{4 s}{6 t})}^{- 2}$

Step 2

Simplify the expression.

Apply the product rule to $\frac{7}{6}$ .

$\frac{7^{2}}{6^{2}} \cdot {(\frac{4 s}{6 t})}^{- 2}$

Raise $7$ to the power of $2$ .

$\frac{49}{6^{2}} \cdot {(\frac{4 s}{6 t})}^{- 2}$

Raise $6$ to the power of $2$ .

$\frac{49}{36} \cdot {(\frac{4 s}{6 t})}^{- 2}$

Step 3

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 s$ .

$\frac{49}{36} \cdot {(\frac{2 (2 s)}{6 t})}^{- 2}$

Cancel the common factors.

Factor $2$ out of $6 t$ .

$\frac{49}{36} \cdot {(\frac{2 (2 s)}{2 (3 t)})}^{- 2}$

Cancel the common factor.

$\frac{49}{36} \cdot {(\frac{2 (2 s)}{2 (3 t)})}^{- 2}$

Rewrite the expression.

$\frac{49}{36} \cdot {(\frac{2 s}{3 t})}^{- 2}$

Step 4

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

$\frac{49}{36} \cdot {(\frac{3 t}{2 s})}^{2}$

Step 5

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

Apply the product rule to $\frac{3 t}{2 s}$ .

$\frac{49}{36} \cdot \frac{{(3 t)}^{2}}{{(2 s)}^{2}}$

Apply the product rule to $3 t$ .

$\frac{49}{36} \cdot \frac{3^{2} t^{2}}{{(2 s)}^{2}}$

Apply the product rule to $2 s$ .

$\frac{49}{36} \cdot \frac{3^{2} t^{2}}{2^{2} s^{2}}$

Step 6

Combine.

$\frac{49 (3^{2} t^{2})}{36 (2^{2} s^{2})}$

Step 7

Simplify the numerator.

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

$\frac{49 \cdot 9 t^{2}}{36 \cdot 2^{2} s^{2}}$

Multiply $49$ by $9$ .

$\frac{441 t^{2}}{36 \cdot 2^{2} s^{2}}$

Step 8

Simplify the denominator.

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

$\frac{441 t^{2}}{36 \cdot 4 s^{2}}$

Multiply $36$ by $4$ .

$\frac{441 t^{2}}{144 s^{2}}$

Step 9

Cancel the common factor of $441$ and $144$ .

Factor $9$ out of $441 t^{2}$ .

$\frac{9 (49 t^{2})}{144 s^{2}}$

Cancel the common factors.

Factor $9$ out of $144 s^{2}$ .

$\frac{9 (49 t^{2})}{9 (16 s^{2})}$

Cancel the common factor.

$\frac{9 (49 t^{2})}{9 (16 s^{2})}$

Rewrite the expression.

$\frac{49 t^{2}}{16 s^{2}}$

Simplify (6/7)^-2*((4s)/(6t))^-2

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