Solve s^6/3t^-2div-s^2/33(-t)^2=

$$\frac { s ^ { 6 } } { 3 t ^ { - 2 } } \div \frac { - s ^ { 2 } } { 33 ( - t ) ^ { 2 } } =$$

Evaluate

$$-11\left(st\right)^{4}$$

Solution Steps

Divide \frac{s^{6}}{3t^{-2}} by \frac{-s^{2}}{33\left(-t\right)^{2}} by multiplying \frac{s^{6}}{3t^{-2}} by the reciprocal of \frac{-s^{2}}{33\left(-t\right)^{2}}.

$$\frac{s^{6}\times 33\left(-t\right)^{2}}{3t^{-2}\left(-s^{2}\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{11\left(-t\right)^{2}s^{6}}{t^{-2}\left(-s^{2}\right)}$$

Calculate -t to the power of 2 and get t^{2}.

$$\frac{11t^{2}s^{6}}{t^{-2}\left(-s^{2}\right)}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{11t^{4}s^{6}}{-s^{2}}$$

Cancel out s^{2} in both numerator and denominator.

$$\frac{11s^{4}t^{4}}{-1}$$

Anything divided by -1 gives its opposite.

$$-11s^{4}t^{4}$$

Expand

$$-11\left(st\right)^{4}$$

Solution Steps

Divide \frac{s^{6}}{3t^{-2}} by \frac{-s^{2}}{33\left(-t\right)^{2}} by multiplying \frac{s^{6}}{3t^{-2}} by the reciprocal of \frac{-s^{2}}{33\left(-t\right)^{2}}.

$$\frac{s^{6}\times 33\left(-t\right)^{2}}{3t^{-2}\left(-s^{2}\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{11\left(-t\right)^{2}s^{6}}{t^{-2}\left(-s^{2}\right)}$$

Calculate -t to the power of 2 and get t^{2}.

$$\frac{11t^{2}s^{6}}{t^{-2}\left(-s^{2}\right)}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{11t^{4}s^{6}}{-s^{2}}$$

Cancel out s^{2} in both numerator and denominator.

$$\frac{11s^{4}t^{4}}{-1}$$

Anything divided by -1 gives its opposite.

$$-11s^{4}t^{4}$$