Solve (x^{3}y^{-4})^{-1}(2^-3x^-1y^-3)^2

$$( x ^ { 3 } y ^ { - 4 } ) ^ { - 1 } ( 2 ^ { - 3 } x ^ { - 1 } y ^ { - 3 } ) ^ { 2 }$$

Evaluate

$$\frac{1}{64y^{2}x^{5}}$$

Solution Steps

Expand \left(x^{3}y^{-4}\right)^{-1}.

$$\left(x^{3}\right)^{-1}\left(y^{-4}\right)^{-1}\times \left(2^{-3}x^{-1}y^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$x^{-3}\left(y^{-4}\right)^{-1}\times \left(2^{-3}x^{-1}y^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -1 to get 4.

$$x^{-3}y^{4}\times \left(2^{-3}x^{-1}y^{-3}\right)^{2}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$x^{-3}y^{4}\times \left(\frac{1}{8}x^{-1}y^{-3}\right)^{2}$$

Expand \left(\frac{1}{8}x^{-1}y^{-3}\right)^{2}.

$$x^{-3}y^{4}\times \left(\frac{1}{8}\right)^{2}\left(x^{-1}\right)^{2}\left(y^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$x^{-3}y^{4}\times \left(\frac{1}{8}\right)^{2}x^{-2}\left(y^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$x^{-3}y^{4}\times \left(\frac{1}{8}\right)^{2}x^{-2}y^{-6}$$

Calculate \frac{1}{8} to the power of 2 and get \frac{1}{64}.

$$x^{-3}y^{4}\times \frac{1}{64}x^{-2}y^{-6}$$

To multiply powers of the same base, add their exponents. Add -3 and -2 to get -5.

$$x^{-5}y^{4}\times \frac{1}{64}y^{-6}$$

To multiply powers of the same base, add their exponents. Add 4 and -6 to get -2.

$$x^{-5}y^{-2}\times \frac{1}{64}$$

Expand

$$\frac{1}{64y^{2}x^{5}}$$

Solution Steps

Expand \left(x^{3}y^{-4}\right)^{-1}.

$$\left(x^{3}\right)^{-1}\left(y^{-4}\right)^{-1}\times \left(2^{-3}x^{-1}y^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$x^{-3}\left(y^{-4}\right)^{-1}\times \left(2^{-3}x^{-1}y^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -1 to get 4.

$$x^{-3}y^{4}\times \left(2^{-3}x^{-1}y^{-3}\right)^{2}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$x^{-3}y^{4}\times \left(\frac{1}{8}x^{-1}y^{-3}\right)^{2}$$

Expand \left(\frac{1}{8}x^{-1}y^{-3}\right)^{2}.

$$x^{-3}y^{4}\times \left(\frac{1}{8}\right)^{2}\left(x^{-1}\right)^{2}\left(y^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$x^{-3}y^{4}\times \left(\frac{1}{8}\right)^{2}x^{-2}\left(y^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$x^{-3}y^{4}\times \left(\frac{1}{8}\right)^{2}x^{-2}y^{-6}$$

Calculate \frac{1}{8} to the power of 2 and get \frac{1}{64}.

$$x^{-3}y^{4}\times \frac{1}{64}x^{-2}y^{-6}$$

To multiply powers of the same base, add their exponents. Add -3 and -2 to get -5.

$$x^{-5}y^{4}\times \frac{1}{64}y^{-6}$$

To multiply powers of the same base, add their exponents. Add 4 and -6 to get -2.

$$x^{-5}y^{-2}\times \frac{1}{64}$$