Solve (a^-2b^2c/a(bc)^2)^2

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

Evaluate

$$\frac{1}{c^{2}a^{6}}$$

Solution Steps

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

$$\left(\frac{cb^{2}}{a^{3}\left(bc\right)^{2}}\right)^{2}$$

Expand \left(bc\right)^{2}.

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

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

$$\left(\frac{1}{ca^{3}}\right)^{2}$$

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

$$\frac{1^{2}}{\left(ca^{3}\right)^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{\left(ca^{3}\right)^{2}}$$

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

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

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

$$\frac{1}{c^{2}a^{6}}$$

Expand

$$\frac{1}{c^{2}a^{6}}$$

Solution Steps

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

$$\left(\frac{cb^{2}}{a^{3}\left(bc\right)^{2}}\right)^{2}$$

Expand \left(bc\right)^{2}.

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

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

$$\left(\frac{1}{ca^{3}}\right)^{2}$$

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

$$\frac{1^{2}}{\left(ca^{3}\right)^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{\left(ca^{3}\right)^{2}}$$

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

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

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

$$\frac{1}{c^{2}a^{6}}$$