Solve frac{(2x^{9}y^-4)^-5}{x^-40y^-25}

$$\frac { ( 2 x ^ { 9 } y ^ { - 4 } ) ^ { - 5 } } { x ^ { - 40 } y ^ { - 25 } }$$

Evaluate

$$\frac{y^{45}}{32x^{5}}$$

Solution Steps

Expand \left(2x^{9}y^{-4}\right)^{-5}.

$$\frac{2^{-5}\left(x^{9}\right)^{-5}\left(y^{-4}\right)^{-5}}{x^{-40}y^{-25}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and -5 to get -45.

$$\frac{2^{-5}x^{-45}\left(y^{-4}\right)^{-5}}{x^{-40}y^{-25}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -5 to get 20.

$$\frac{2^{-5}x^{-45}y^{20}}{x^{-40}y^{-25}}$$

Calculate 2 to the power of -5 and get \frac{1}{32}.

$$\frac{\frac{1}{32}x^{-45}y^{20}}{x^{-40}y^{-25}}$$

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

$$\frac{\frac{1}{32}x^{-45}y^{45}}{x^{-40}}$$

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

$$\frac{\frac{1}{32}y^{45}}{x^{5}}$$

Expand

$$\frac{y^{45}}{32x^{5}}$$

Solution Steps

Expand \left(2x^{9}y^{-4}\right)^{-5}.

$$\frac{2^{-5}\left(x^{9}\right)^{-5}\left(y^{-4}\right)^{-5}}{x^{-40}y^{-25}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and -5 to get -45.

$$\frac{2^{-5}x^{-45}\left(y^{-4}\right)^{-5}}{x^{-40}y^{-25}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -5 to get 20.

$$\frac{2^{-5}x^{-45}y^{20}}{x^{-40}y^{-25}}$$

Calculate 2 to the power of -5 and get \frac{1}{32}.

$$\frac{\frac{1}{32}x^{-45}y^{20}}{x^{-40}y^{-25}}$$

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

$$\frac{\frac{1}{32}x^{-45}y^{45}}{x^{-40}}$$

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

$$\frac{\frac{1}{32}y^{45}}{x^{5}}$$