Solve (3x^-3)^5/(3x^-3)^8=

$$\frac { ( 3 x ^ { - 3 } ) ^ { 5 } } { ( 3 x ^ { - 3 } ) ^ { 8 } } =$$

Evaluate

$$\frac{x^{9}}{27}$$

Solution Steps

Rewrite \left(3x^{-3}\right)^{8} as \left(3x^{-3}\right)^{5}\times \left(3x^{-3}\right)^{3}. Cancel out \left(3x^{-3}\right)^{5} in both numerator and denominator.

$$\frac{1}{\left(3x^{-3}\right)^{3}}$$

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

$$\frac{1}{3^{3}\left(x^{-3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{1}{3^{3}x^{-9}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{1}{27x^{-9}}$$

Expand

$$\frac{x^{9}}{27}$$

Solution Steps

Rewrite \left(3x^{-3}\right)^{8} as \left(3x^{-3}\right)^{5}\times \left(3x^{-3}\right)^{3}. Cancel out \left(3x^{-3}\right)^{5} in both numerator and denominator.

$$\frac{1}{\left(3x^{-3}\right)^{3}}$$

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

$$\frac{1}{3^{3}\left(x^{-3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{1}{3^{3}x^{-9}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{1}{27x^{-9}}$$