Solve (2x^6/y^4)^-3quad1/8x

$$( \frac { 2 x ^ { 6 } } { y ^ { 4 } } ) ^ { - 3 } \quad 1 / 8 x$$

Evaluate

$$\frac{y^{12}}{64x^{17}}$$

Solution Steps

To raise \frac{2x^{6}}{y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(2x^{6}\right)^{-3}}{\left(y^{4}\right)^{-3}} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

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

Express \frac{\left(2x^{6}\right)^{-3}}{\left(y^{4}\right)^{-3}\times 8}x as a single fraction.

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

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

$$\frac{\left(2x^{6}\right)^{-3}x}{y^{-12}\times 8}$$

Expand \left(2x^{6}\right)^{-3}.

$$\frac{2^{-3}\left(x^{6}\right)^{-3}x}{y^{-12}\times 8}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{2^{-3}x^{-18}x}{y^{-12}\times 8}$$

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

$$\frac{\frac{1}{8}x^{-18}x}{y^{-12}\times 8}$$

To multiply powers of the same base, add their exponents. Add -18 and 1 to get -17.

$$\frac{\frac{1}{8}x^{-17}}{y^{-12}\times 8}$$

Expand

$$\frac{y^{12}}{64x^{17}}$$

Solution Steps

To raise \frac{2x^{6}}{y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(2x^{6}\right)^{-3}}{\left(y^{4}\right)^{-3}} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

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

Express \frac{\left(2x^{6}\right)^{-3}}{\left(y^{4}\right)^{-3}\times 8}x as a single fraction.

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

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

$$\frac{\left(2x^{6}\right)^{-3}x}{y^{-12}\times 8}$$

Expand \left(2x^{6}\right)^{-3}.

$$\frac{2^{-3}\left(x^{6}\right)^{-3}x}{y^{-12}\times 8}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{2^{-3}x^{-18}x}{y^{-12}\times 8}$$

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

$$\frac{\frac{1}{8}x^{-18}x}{y^{-12}\times 8}$$

To multiply powers of the same base, add their exponents. Add -18 and 1 to get -17.

$$\frac{\frac{1}{8}x^{-17}}{y^{-12}\times 8}$$