Solve 1/9c^{8}(d^-6/d^-9c^-8)^3

$$\frac { 1 } { 9 } c ^ { 8 } ( \frac { d ^ { - 6 } } { d ^ { - 9 } c ^ { - 8 } } ) ^ { 3 }$$

Evaluate

$$\frac{d^{9}c^{32}}{9}$$

Solution Steps

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

$$\frac{1}{9}c^{8}\times \left(\frac{d^{3}}{c^{-8}}\right)^{3}$$

To raise \frac{d^{3}}{c^{-8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1}{9}c^{8}\times \frac{\left(d^{3}\right)^{3}}{\left(c^{-8}\right)^{3}}$$

Multiply \frac{1}{9} times \frac{\left(d^{3}\right)^{3}}{\left(c^{-8}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(d^{3}\right)^{3}}{9\left(c^{-8}\right)^{3}}c^{8}$$

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

$$\frac{d^{9}}{9\left(c^{-8}\right)^{3}}c^{8}$$

To raise a power to another power, multiply the exponents. Multiply -8 and 3 to get -24.

$$\frac{d^{9}}{9c^{-24}}c^{8}$$

Express \frac{d^{9}}{9c^{-24}}c^{8} as a single fraction.

$$\frac{d^{9}c^{8}}{9c^{-24}}$$

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

$$\frac{d^{9}c^{32}}{9}$$

Expand

$$\frac{d^{9}c^{32}}{9}$$

Solution Steps

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

$$\frac{1}{9}c^{8}\times \left(\frac{d^{3}}{c^{-8}}\right)^{3}$$

To raise \frac{d^{3}}{c^{-8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1}{9}c^{8}\times \frac{\left(d^{3}\right)^{3}}{\left(c^{-8}\right)^{3}}$$

Multiply \frac{1}{9} times \frac{\left(d^{3}\right)^{3}}{\left(c^{-8}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(d^{3}\right)^{3}}{9\left(c^{-8}\right)^{3}}c^{8}$$

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

$$\frac{d^{9}}{9\left(c^{-8}\right)^{3}}c^{8}$$

To raise a power to another power, multiply the exponents. Multiply -8 and 3 to get -24.

$$\frac{d^{9}}{9c^{-24}}c^{8}$$

Express \frac{d^{9}}{9c^{-24}}c^{8} as a single fraction.

$$\frac{d^{9}c^{8}}{9c^{-24}}$$

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

$$\frac{d^{9}c^{32}}{9}$$