Solve ((ab^2c)^-3/b^-3)^3

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

Evaluate

$$\frac{1}{\left(abc\right)^{9}}$$

Solution Steps

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

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

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

$$\left(\frac{a^{-3}b^{-6}c^{-3}}{b^{-3}}\right)^{3}$$

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

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

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

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

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

$$\frac{\left(a^{-3}c^{-3}\right)^{3}}{b^{9}}$$

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

$$\frac{\left(a^{-3}\right)^{3}\left(c^{-3}\right)^{3}}{b^{9}}$$

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

$$\frac{a^{-9}\left(c^{-3}\right)^{3}}{b^{9}}$$

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

$$\frac{a^{-9}c^{-9}}{b^{9}}$$

Expand

$$\frac{1}{\left(abc\right)^{9}}$$

Solution Steps

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

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

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

$$\left(\frac{a^{-3}b^{-6}c^{-3}}{b^{-3}}\right)^{3}$$

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

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

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

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

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

$$\frac{\left(a^{-3}c^{-3}\right)^{3}}{b^{9}}$$

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

$$\frac{\left(a^{-3}\right)^{3}\left(c^{-3}\right)^{3}}{b^{9}}$$

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

$$\frac{a^{-9}\left(c^{-3}\right)^{3}}{b^{9}}$$

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

$$\frac{a^{-9}c^{-9}}{b^{9}}$$