Solve -x^{3}y^-4*(2x^-2y^5)^4

$$- x ^ { 3 } y ^ { - 4 } \cdot ( 2 x ^ { - 2 } y ^ { 5 } ) ^ { 4 }$$

Evaluate

$$-\frac{16y^{16}}{x^{5}}$$

Solution Steps

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

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

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

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

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

$$\left(-x^{3}\right)y^{-4}\times 2^{4}x^{-8}y^{20}$$

Calculate 2 to the power of 4 and get 16.

$$\left(-x^{3}\right)y^{-4}\times 16x^{-8}y^{20}$$

To multiply powers of the same base, add their exponents. Add -4 and 20 to get 16.

$$\left(-x^{3}\right)y^{16}\times 16x^{-8}$$

Multiply -1 and 16 to get -16.

$$-16x^{3}y^{16}x^{-8}$$

To multiply powers of the same base, add their exponents. Add 3 and -8 to get -5.

$$-16x^{-5}y^{16}$$

Expand

$$-\frac{16y^{16}}{x^{5}}$$

Solution Steps

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

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

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

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

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

$$\left(-x^{3}\right)y^{-4}\times 2^{4}x^{-8}y^{20}$$

Calculate 2 to the power of 4 and get 16.

$$\left(-x^{3}\right)y^{-4}\times 16x^{-8}y^{20}$$

To multiply powers of the same base, add their exponents. Add -4 and 20 to get 16.

$$\left(-x^{3}\right)y^{16}\times 16x^{-8}$$

Multiply -1 and 16 to get -16.

$$-16x^{3}y^{16}x^{-8}$$

To multiply powers of the same base, add their exponents. Add 3 and -8 to get -5.

$$-16x^{-5}y^{16}$$