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

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

Evaluate

$$\frac{b^{4}}{c}$$

Solution Steps

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

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

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

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

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

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

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

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

Expand \left(a^{-4}b^{-2}c^{-3}\right)^{-1}.

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

To raise a power to another power, multiply the exponents. Multiply -4 and -1 to get 4.

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

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

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

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

$$\frac{a^{4}b^{6}c^{2}}{a^{4}b^{2}c^{3}}$$

Cancel out b^{2}c^{2}a^{4} in both numerator and denominator.

$$\frac{b^{4}}{c}$$

Expand

$$\frac{b^{4}}{c}$$

Solution Steps

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

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

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

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

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

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

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

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

Expand \left(a^{-4}b^{-2}c^{-3}\right)^{-1}.

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

To raise a power to another power, multiply the exponents. Multiply -4 and -1 to get 4.

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

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

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

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

$$\frac{a^{4}b^{6}c^{2}}{a^{4}b^{2}c^{3}}$$

Cancel out b^{2}c^{2}a^{4} in both numerator and denominator.

$$\frac{b^{4}}{c}$$