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

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

Evaluate

$$\frac{9c^{12}}{4a^{2}b^{6}}$$

Solution Steps

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

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

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

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

Calculate a to the power of 1 and get a.

$$\left(\frac{2ab^{3}}{3c^{6}}\right)^{-2}$$

To raise \frac{2ab^{3}}{3c^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2ab^{3}\right)^{-2}}{\left(3c^{6}\right)^{-2}}$$

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

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

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

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

Calculate 2 to the power of -2 and get \frac{1}{4}.

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

Expand \left(3c^{6}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{3^{-2}c^{-12}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{\frac{1}{9}c^{-12}}$$

Expand

$$\frac{9c^{12}}{4a^{2}b^{6}}$$

Solution Steps

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

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

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

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

Calculate a to the power of 1 and get a.

$$\left(\frac{2ab^{3}}{3c^{6}}\right)^{-2}$$

To raise \frac{2ab^{3}}{3c^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2ab^{3}\right)^{-2}}{\left(3c^{6}\right)^{-2}}$$

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

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

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

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

Calculate 2 to the power of -2 and get \frac{1}{4}.

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

Expand \left(3c^{6}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{3^{-2}c^{-12}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{\frac{1}{9}c^{-12}}$$