Solve (frac{3x^{2}y^3}{6x^-5y^3})^-2

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

Evaluate

$$\frac{4}{x^{14}}$$

Solution Steps

Cancel out 3y^{3} in both numerator and denominator.

$$\left(\frac{x^{2}}{2x^{-5}}\right)^{-2}$$

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

$$\left(\frac{x^{7}}{2}\right)^{-2}$$

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

$$\frac{\left(x^{7}\right)^{-2}}{2^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

$$\frac{x^{-14}}{2^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{x^{-14}}{\frac{1}{4}}$$

Divide x^{-14} by \frac{1}{4} by multiplying x^{-14} by the reciprocal of \frac{1}{4}.

$$x^{-14}\times 4$$

Expand

$$\frac{4}{x^{14}}$$

Solution Steps

Cancel out 3y^{3} in both numerator and denominator.

$$\left(\frac{x^{2}}{2x^{-5}}\right)^{-2}$$

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

$$\left(\frac{x^{7}}{2}\right)^{-2}$$

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

$$\frac{\left(x^{7}\right)^{-2}}{2^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

$$\frac{x^{-14}}{2^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{x^{-14}}{\frac{1}{4}}$$

Divide x^{-14} by \frac{1}{4} by multiplying x^{-14} by the reciprocal of \frac{1}{4}.

$$x^{-14}\times 4$$