Solve (6x^{-3}y^6)(3x^-2y^-1)^2

$$( 6 x ^ { - 3 } y ^ { 6 } ) ( 3 x ^ { - 2 } y ^ { - 1 } ) ^ { 2 }$$

Evaluate

$$\frac{54y^{4}}{x^{7}}$$

Solution Steps

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$6x^{-3}y^{6}\times 9x^{-4}y^{-2}$$

Multiply 6 and 9 to get 54.

$$54x^{-3}y^{6}x^{-4}y^{-2}$$

To multiply powers of the same base, add their exponents. Add -3 and -4 to get -7.

$$54x^{-7}y^{6}y^{-2}$$

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

$$54x^{-7}y^{4}$$

Expand

$$\frac{54y^{4}}{x^{7}}$$

Solution Steps

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$6x^{-3}y^{6}\times 9x^{-4}y^{-2}$$

Multiply 6 and 9 to get 54.

$$54x^{-3}y^{6}x^{-4}y^{-2}$$

To multiply powers of the same base, add their exponents. Add -3 and -4 to get -7.

$$54x^{-7}y^{6}y^{-2}$$

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

$$54x^{-7}y^{4}$$