Solve (frac{4s^{5}t^-7}{-2s^-2t^4})^3

$$( \frac { 4 s ^ { 5 } t ^ { - 7 } } { - 2 s ^ { - 2 } t ^ { 4 } } ) ^ { 3 }$$

Evaluate

$$-\frac{8s^{21}}{t^{33}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\left(\frac{2t^{-7}s^{5}}{-s^{-2}t^{4}}\right)^{3}$$

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

$$\left(\frac{2t^{-7}s^{7}}{-t^{4}}\right)^{3}$$

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

$$\left(\frac{2s^{7}}{-t^{11}}\right)^{3}$$

Cancel out -1 in both numerator and denominator.

$$\left(\frac{-2s^{7}}{t^{11}}\right)^{3}$$

To raise \frac{-2s^{7}}{t^{11}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-2s^{7}\right)^{3}}{\left(t^{11}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 11 and 3 to get 33.

$$\frac{\left(-2s^{7}\right)^{3}}{t^{33}}$$

Expand \left(-2s^{7}\right)^{3}.

$$\frac{\left(-2\right)^{3}\left(s^{7}\right)^{3}}{t^{33}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{\left(-2\right)^{3}s^{21}}{t^{33}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8s^{21}}{t^{33}}$$

Expand

$$-\frac{8s^{21}}{t^{33}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\left(\frac{2t^{-7}s^{5}}{-s^{-2}t^{4}}\right)^{3}$$

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

$$\left(\frac{2t^{-7}s^{7}}{-t^{4}}\right)^{3}$$

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

$$\left(\frac{2s^{7}}{-t^{11}}\right)^{3}$$

Cancel out -1 in both numerator and denominator.

$$\left(\frac{-2s^{7}}{t^{11}}\right)^{3}$$

To raise \frac{-2s^{7}}{t^{11}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-2s^{7}\right)^{3}}{\left(t^{11}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 11 and 3 to get 33.

$$\frac{\left(-2s^{7}\right)^{3}}{t^{33}}$$

Expand \left(-2s^{7}\right)^{3}.

$$\frac{\left(-2\right)^{3}\left(s^{7}\right)^{3}}{t^{33}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{\left(-2\right)^{3}s^{21}}{t^{33}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8s^{21}}{t^{33}}$$