Solve frac{(2x^{-3}y^{-2})^5}{(6x^-4y^-8)^2}

$$\frac { ( 2 x ^ { - 3 } y ^ { - 2 } ) ^ { 5 } } { ( 6 x ^ { - 4 } y ^ { - 8 } ) ^ { 2 } }$$

Evaluate

$$\frac{8y^{6}}{9x^{7}}$$

Solution Steps

Expand \left(2x^{-3}y^{-2}\right)^{5}.

$$\frac{2^{5}\left(x^{-3}\right)^{5}\left(y^{-2}\right)^{5}}{\left(6x^{-4}y^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 5 to get -15.

$$\frac{2^{5}x^{-15}\left(y^{-2}\right)^{5}}{\left(6x^{-4}y^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 5 to get -10.

$$\frac{2^{5}x^{-15}y^{-10}}{\left(6x^{-4}y^{-8}\right)^{2}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32x^{-15}y^{-10}}{\left(6x^{-4}y^{-8}\right)^{2}}$$

Expand \left(6x^{-4}y^{-8}\right)^{2}.

$$\frac{32x^{-15}y^{-10}}{6^{2}\left(x^{-4}\right)^{2}\left(y^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 2 to get -8.

$$\frac{32x^{-15}y^{-10}}{6^{2}x^{-8}\left(y^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -8 and 2 to get -16.

$$\frac{32x^{-15}y^{-10}}{6^{2}x^{-8}y^{-16}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{32x^{-15}y^{-10}}{36x^{-8}y^{-16}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{8x^{-15}y^{-10}}{9y^{-16}x^{-8}}$$

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

$$\frac{8x^{-15}y^{6}}{9x^{-8}}$$

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

$$\frac{8y^{6}}{9x^{7}}$$

Expand

$$\frac{8y^{6}}{9x^{7}}$$

Solution Steps

Expand \left(2x^{-3}y^{-2}\right)^{5}.

$$\frac{2^{5}\left(x^{-3}\right)^{5}\left(y^{-2}\right)^{5}}{\left(6x^{-4}y^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 5 to get -15.

$$\frac{2^{5}x^{-15}\left(y^{-2}\right)^{5}}{\left(6x^{-4}y^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 5 to get -10.

$$\frac{2^{5}x^{-15}y^{-10}}{\left(6x^{-4}y^{-8}\right)^{2}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32x^{-15}y^{-10}}{\left(6x^{-4}y^{-8}\right)^{2}}$$

Expand \left(6x^{-4}y^{-8}\right)^{2}.

$$\frac{32x^{-15}y^{-10}}{6^{2}\left(x^{-4}\right)^{2}\left(y^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 2 to get -8.

$$\frac{32x^{-15}y^{-10}}{6^{2}x^{-8}\left(y^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -8 and 2 to get -16.

$$\frac{32x^{-15}y^{-10}}{6^{2}x^{-8}y^{-16}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{32x^{-15}y^{-10}}{36x^{-8}y^{-16}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{8x^{-15}y^{-10}}{9y^{-16}x^{-8}}$$

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

$$\frac{8x^{-15}y^{6}}{9x^{-8}}$$

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

$$\frac{8y^{6}}{9x^{7}}$$