Solve (frac{9a^{-3}b^{-8}c^{3}}{81a^-1b^-6c^5})^-3

$$( \frac { 9 a ^ { - 3 } b ^ { - 8 } c ^ { 3 } } { 81 a ^ { - 1 } b ^ { - 6 } c ^ { 5 } } ) ^ { - 3 }$$

Evaluate

$$729\left(abc\right)^{6}$$

Solution Steps

Cancel out 9c^{3} in both numerator and denominator.

$$\left(\frac{b^{-8}a^{-3}}{9b^{-6}\times \frac{1}{a}c^{2}}\right)^{-3}$$

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

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

To raise \frac{1}{9a^{2}b^{2}c^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 1 to the power of -3 and get 1.

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

Expand \left(9a^{2}b^{2}c^{2}\right)^{-3}.

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

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

$$\frac{1}{9^{-3}a^{-6}\left(b^{2}\right)^{-3}\left(c^{2}\right)^{-3}}$$

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

$$\frac{1}{9^{-3}a^{-6}b^{-6}\left(c^{2}\right)^{-3}}$$

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

$$\frac{1}{9^{-3}a^{-6}b^{-6}c^{-6}}$$

Calculate 9 to the power of -3 and get \frac{1}{729}.

$$\frac{1}{\frac{1}{729}a^{-6}b^{-6}c^{-6}}$$

Expand

$$729\left(abc\right)^{6}$$

Solution Steps

Cancel out 9c^{3} in both numerator and denominator.

$$\left(\frac{b^{-8}a^{-3}}{9b^{-6}\times \frac{1}{a}c^{2}}\right)^{-3}$$

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

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

To raise \frac{1}{9a^{2}b^{2}c^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 1 to the power of -3 and get 1.

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

Expand \left(9a^{2}b^{2}c^{2}\right)^{-3}.

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

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

$$\frac{1}{9^{-3}a^{-6}\left(b^{2}\right)^{-3}\left(c^{2}\right)^{-3}}$$

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

$$\frac{1}{9^{-3}a^{-6}b^{-6}\left(c^{2}\right)^{-3}}$$

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

$$\frac{1}{9^{-3}a^{-6}b^{-6}c^{-6}}$$

Calculate 9 to the power of -3 and get \frac{1}{729}.

$$\frac{1}{\frac{1}{729}a^{-6}b^{-6}c^{-6}}$$