Solve 6x^3*(2x^5y^-4)^-3

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

Evaluate

$$\frac{3\times \left(\frac{y}{x}\right)^{12}}{4}$$

Solution Steps

Expand \left(2x^{5}y^{-4}\right)^{-3}.

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

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

$$6x^{3}\times 2^{-3}x^{-15}\left(y^{-4}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -3 to get 12.

$$6x^{3}\times 2^{-3}x^{-15}y^{12}$$

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

$$6x^{3}\times \frac{1}{8}x^{-15}y^{12}$$

Multiply 6 and \frac{1}{8} to get \frac{3}{4}.

$$\frac{3}{4}x^{3}x^{-15}y^{12}$$

To multiply powers of the same base, add their exponents. Add 3 and -15 to get -12.

$$\frac{3}{4}x^{-12}y^{12}$$

Expand

$$\frac{3\times \left(\frac{y}{x}\right)^{12}}{4}$$

Solution Steps

Expand \left(2x^{5}y^{-4}\right)^{-3}.

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

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

$$6x^{3}\times 2^{-3}x^{-15}\left(y^{-4}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -3 to get 12.

$$6x^{3}\times 2^{-3}x^{-15}y^{12}$$

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

$$6x^{3}\times \frac{1}{8}x^{-15}y^{12}$$

Multiply 6 and \frac{1}{8} to get \frac{3}{4}.

$$\frac{3}{4}x^{3}x^{-15}y^{12}$$

To multiply powers of the same base, add their exponents. Add 3 and -15 to get -12.

$$\frac{3}{4}x^{-12}y^{12}$$