Solve (1/c^{3}b^{2})^-1(-3c^2b^7)^3

$$( 1 / c ^ { 3 } b ^ { 2 } ) ^ { - 1 } ( - 3 c ^ { 2 } b ^ { 7 } ) ^ { 3 }$$

Evaluate

$$-27c^{9}b^{19}$$

Solution Steps

Express \frac{1}{c^{3}}b^{2} as a single fraction.

$$\left(\frac{b^{2}}{c^{3}}\right)^{-1}\left(-3c^{2}b^{7}\right)^{3}$$

To raise \frac{b^{2}}{c^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-3c^{2}b^{7}\right)^{3}$$

Expand \left(-3c^{2}b^{7}\right)^{3}.

$$\frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-3\right)^{3}\left(c^{2}\right)^{3}\left(b^{7}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-3\right)^{3}c^{6}\left(b^{7}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-3\right)^{3}c^{6}b^{21}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-27\right)c^{6}b^{21}$$

Express \frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-27\right) as a single fraction.

$$\frac{-\left(b^{2}\right)^{-1}\times 27}{\left(c^{3}\right)^{-1}}c^{6}b^{21}$$

Express \frac{-\left(b^{2}\right)^{-1}\times 27}{\left(c^{3}\right)^{-1}}c^{6} as a single fraction.

$$\frac{-\left(b^{2}\right)^{-1}\times 27c^{6}}{\left(c^{3}\right)^{-1}}b^{21}$$

Express \frac{-\left(b^{2}\right)^{-1}\times 27c^{6}}{\left(c^{3}\right)^{-1}}b^{21} as a single fraction.

$$\frac{-\left(b^{2}\right)^{-1}\times 27c^{6}b^{21}}{\left(c^{3}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{-b^{-2}\times 27c^{6}b^{21}}{\left(c^{3}\right)^{-1}}$$

To multiply powers of the same base, add their exponents. Add -2 and 21 to get 19.

$$\frac{-b^{19}\times 27c^{6}}{\left(c^{3}\right)^{-1}}$$

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

$$\frac{-b^{19}\times 27c^{6}}{c^{-3}}$$

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

$$-27c^{9}b^{19}$$

Expand

$$-27c^{9}b^{19}$$

Solution Steps

Express \frac{1}{c^{3}}b^{2} as a single fraction.

$$\left(\frac{b^{2}}{c^{3}}\right)^{-1}\left(-3c^{2}b^{7}\right)^{3}$$

To raise \frac{b^{2}}{c^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-3c^{2}b^{7}\right)^{3}$$

Expand \left(-3c^{2}b^{7}\right)^{3}.

$$\frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-3\right)^{3}\left(c^{2}\right)^{3}\left(b^{7}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-3\right)^{3}c^{6}\left(b^{7}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-3\right)^{3}c^{6}b^{21}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-27\right)c^{6}b^{21}$$

Express \frac{\left(b^{2}\right)^{-1}}{\left(c^{3}\right)^{-1}}\left(-27\right) as a single fraction.

$$\frac{-\left(b^{2}\right)^{-1}\times 27}{\left(c^{3}\right)^{-1}}c^{6}b^{21}$$

Express \frac{-\left(b^{2}\right)^{-1}\times 27}{\left(c^{3}\right)^{-1}}c^{6} as a single fraction.

$$\frac{-\left(b^{2}\right)^{-1}\times 27c^{6}}{\left(c^{3}\right)^{-1}}b^{21}$$

Express \frac{-\left(b^{2}\right)^{-1}\times 27c^{6}}{\left(c^{3}\right)^{-1}}b^{21} as a single fraction.

$$\frac{-\left(b^{2}\right)^{-1}\times 27c^{6}b^{21}}{\left(c^{3}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{-b^{-2}\times 27c^{6}b^{21}}{\left(c^{3}\right)^{-1}}$$

To multiply powers of the same base, add their exponents. Add -2 and 21 to get 19.

$$\frac{-b^{19}\times 27c^{6}}{\left(c^{3}\right)^{-1}}$$

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

$$\frac{-b^{19}\times 27c^{6}}{c^{-3}}$$

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

$$-27c^{9}b^{19}$$