Solve left(3x^8y^-8right)^-2/3x^-8{y^8}

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

Evaluate

$$\frac{\left(\frac{y}{x}\right)^{8}}{27}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 8 and -2 to get -16.

$$\frac{3^{-2}x^{-16}\left(y^{-8}\right)^{-2}}{3x^{-8}y^{8}}$$

To raise a power to another power, multiply the exponents. Multiply -8 and -2 to get 16.

$$\frac{3^{-2}x^{-16}y^{16}}{3x^{-8}y^{8}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}x^{-16}y^{16}}{3x^{-8}y^{8}}$$

Cancel out y^{8} in both numerator and denominator.

$$\frac{\frac{1}{9}x^{-16}y^{8}}{3x^{-8}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\frac{1}{9}y^{8}}{3x^{8}}$$

Expand

$$\frac{\left(\frac{y}{x}\right)^{8}}{27}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 8 and -2 to get -16.

$$\frac{3^{-2}x^{-16}\left(y^{-8}\right)^{-2}}{3x^{-8}y^{8}}$$

To raise a power to another power, multiply the exponents. Multiply -8 and -2 to get 16.

$$\frac{3^{-2}x^{-16}y^{16}}{3x^{-8}y^{8}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}x^{-16}y^{16}}{3x^{-8}y^{8}}$$

Cancel out y^{8} in both numerator and denominator.

$$\frac{\frac{1}{9}x^{-16}y^{8}}{3x^{-8}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\frac{1}{9}y^{8}}{3x^{8}}$$