Solve (frac{a^{-9}b^{2}c^-2}{a^-6b^5c})^-2

$$( \frac { a ^ { - 9 } b ^ { 2 } c ^ { - 2 } } { a ^ { - 6 } b ^ { 5 } c } ) ^ { - 2 }$$

Evaluate

$$\left(abc\right)^{6}$$

Solution Steps

Cancel out b^{2} in both numerator and denominator.

$$\left(\frac{a^{-9}c^{-2}}{a^{-6}cb^{3}}\right)^{-2}$$

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

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

To raise \frac{1}{a^{3}b^{3}c^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 1 to the power of -2 and get 1.

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

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

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

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

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

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

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

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

$$\frac{1}{a^{-6}b^{-6}c^{-6}}$$

Expand

$$\left(abc\right)^{6}$$

Solution Steps

Cancel out b^{2} in both numerator and denominator.

$$\left(\frac{a^{-9}c^{-2}}{a^{-6}cb^{3}}\right)^{-2}$$

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

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

To raise \frac{1}{a^{3}b^{3}c^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 1 to the power of -2 and get 1.

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

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

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

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

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

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

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

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

$$\frac{1}{a^{-6}b^{-6}c^{-6}}$$