Solve frac{(3a^{-4}b^{-9}c^{4})^{2}}{(3^{-1}a^3b^6c^-2)^-3}

$$\frac { ( 3 a ^ { - 4 } b ^ { - 9 } c ^ { 4 } ) ^ { 2 } } { ( 3 ^ { - 1 } a ^ { 3 } b ^ { 6 } c ^ { - 2 } ) ^ { - 3 } }$$

Evaluate

$$\frac{ac^{2}}{3}$$

Solution Steps

Expand \left(3a^{-4}b^{-9}c^{4}\right)^{2}.

$$\frac{3^{2}\left(a^{-4}\right)^{2}\left(b^{-9}\right)^{2}\left(c^{4}\right)^{2}}{\left(3^{-1}a^{3}b^{6}c^{-2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 2 to get -8.

$$\frac{3^{2}a^{-8}\left(b^{-9}\right)^{2}\left(c^{4}\right)^{2}}{\left(3^{-1}a^{3}b^{6}c^{-2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -9 and 2 to get -18.

$$\frac{3^{2}a^{-8}b^{-18}\left(c^{4}\right)^{2}}{\left(3^{-1}a^{3}b^{6}c^{-2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{3^{2}a^{-8}b^{-18}c^{8}}{\left(3^{-1}a^{3}b^{6}c^{-2}\right)^{-3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(3^{-1}a^{3}b^{6}c^{-2}\right)^{-3}}$$

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

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(\frac{1}{3}a^{3}b^{6}c^{-2}\right)^{-3}}$$

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

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(\frac{1}{3}\right)^{-3}\left(a^{3}\right)^{-3}\left(b^{6}\right)^{-3}\left(c^{-2}\right)^{-3}}$$

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

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(\frac{1}{3}\right)^{-3}a^{-9}\left(b^{6}\right)^{-3}\left(c^{-2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(\frac{1}{3}\right)^{-3}a^{-9}b^{-18}\left(c^{-2}\right)^{-3}}$$

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

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(\frac{1}{3}\right)^{-3}a^{-9}b^{-18}c^{6}}$$

Calculate \frac{1}{3} to the power of -3 and get 27.

$$\frac{9a^{-8}b^{-18}c^{8}}{27a^{-9}b^{-18}c^{6}}$$

Cancel out 9b^{-18}c^{6} in both numerator and denominator.

$$\frac{a^{-8}c^{2}}{3a^{-9}}$$

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

$$\frac{a^{1}c^{2}}{3}$$

Calculate a to the power of 1 and get a.

$$\frac{ac^{2}}{3}$$

Expand

$$\frac{ac^{2}}{3}$$

Solution Steps

Expand \left(3a^{-4}b^{-9}c^{4}\right)^{2}.

$$\frac{3^{2}\left(a^{-4}\right)^{2}\left(b^{-9}\right)^{2}\left(c^{4}\right)^{2}}{\left(3^{-1}a^{3}b^{6}c^{-2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 2 to get -8.

$$\frac{3^{2}a^{-8}\left(b^{-9}\right)^{2}\left(c^{4}\right)^{2}}{\left(3^{-1}a^{3}b^{6}c^{-2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -9 and 2 to get -18.

$$\frac{3^{2}a^{-8}b^{-18}\left(c^{4}\right)^{2}}{\left(3^{-1}a^{3}b^{6}c^{-2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{3^{2}a^{-8}b^{-18}c^{8}}{\left(3^{-1}a^{3}b^{6}c^{-2}\right)^{-3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(3^{-1}a^{3}b^{6}c^{-2}\right)^{-3}}$$

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

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(\frac{1}{3}a^{3}b^{6}c^{-2}\right)^{-3}}$$

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

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(\frac{1}{3}\right)^{-3}\left(a^{3}\right)^{-3}\left(b^{6}\right)^{-3}\left(c^{-2}\right)^{-3}}$$

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

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(\frac{1}{3}\right)^{-3}a^{-9}\left(b^{6}\right)^{-3}\left(c^{-2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(\frac{1}{3}\right)^{-3}a^{-9}b^{-18}\left(c^{-2}\right)^{-3}}$$

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

$$\frac{9a^{-8}b^{-18}c^{8}}{\left(\frac{1}{3}\right)^{-3}a^{-9}b^{-18}c^{6}}$$

Calculate \frac{1}{3} to the power of -3 and get 27.

$$\frac{9a^{-8}b^{-18}c^{8}}{27a^{-9}b^{-18}c^{6}}$$

Cancel out 9b^{-18}c^{6} in both numerator and denominator.

$$\frac{a^{-8}c^{2}}{3a^{-9}}$$

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

$$\frac{a^{1}c^{2}}{3}$$

Calculate a to the power of 1 and get a.

$$\frac{ac^{2}}{3}$$