Solve (3bc^-2)^-2/(3b^-3c)^-1

$$\frac { ( 3 b c ^ { - 2 } ) ^ { - 2 } } { ( 3 b ^ { - 3 } c ) ^ { - 1 } }$$

Evaluate

$$\frac{\left(\frac{c}{b}\right)^{5}}{3}$$

Solution Steps

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

$$\frac{3^{-2}b^{-2}\left(c^{-2}\right)^{-2}}{\left(3b^{-3}c\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -2 to get 4.

$$\frac{3^{-2}b^{-2}c^{4}}{\left(3b^{-3}c\right)^{-1}}$$

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

$$\frac{\frac{1}{9}b^{-2}c^{4}}{\left(3b^{-3}c\right)^{-1}}$$

Expand \left(3b^{-3}c\right)^{-1}.

$$\frac{\frac{1}{9}b^{-2}c^{4}}{3^{-1}\left(b^{-3}\right)^{-1}c^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -1 to get 3.

$$\frac{\frac{1}{9}b^{-2}c^{4}}{3^{-1}b^{3}c^{-1}}$$

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

$$\frac{\frac{1}{9}b^{-2}c^{4}}{\frac{1}{3}b^{3}c^{-1}}$$

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

$$\frac{\frac{1}{9}b^{-2}c^{5}}{\frac{1}{3}b^{3}}$$

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

$$\frac{\frac{1}{9}c^{5}}{\frac{1}{3}b^{5}}$$

Expand

$$\frac{\left(\frac{c}{b}\right)^{5}}{3}$$

Solution Steps

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

$$\frac{3^{-2}b^{-2}\left(c^{-2}\right)^{-2}}{\left(3b^{-3}c\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -2 to get 4.

$$\frac{3^{-2}b^{-2}c^{4}}{\left(3b^{-3}c\right)^{-1}}$$

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

$$\frac{\frac{1}{9}b^{-2}c^{4}}{\left(3b^{-3}c\right)^{-1}}$$

Expand \left(3b^{-3}c\right)^{-1}.

$$\frac{\frac{1}{9}b^{-2}c^{4}}{3^{-1}\left(b^{-3}\right)^{-1}c^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -1 to get 3.

$$\frac{\frac{1}{9}b^{-2}c^{4}}{3^{-1}b^{3}c^{-1}}$$

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

$$\frac{\frac{1}{9}b^{-2}c^{4}}{\frac{1}{3}b^{3}c^{-1}}$$

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

$$\frac{\frac{1}{9}b^{-2}c^{5}}{\frac{1}{3}b^{3}}$$

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

$$\frac{\frac{1}{9}c^{5}}{\frac{1}{3}b^{5}}$$