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

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

Evaluate

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

Solution Steps

Cancel out c in both numerator and denominator.

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

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

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

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

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

Calculate b to the power of 1 and get b.

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

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

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

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

$$\frac{a^{6}}{\left(bc^{2}\right)^{2}}$$

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

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

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

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

Expand

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

Solution Steps

Cancel out c in both numerator and denominator.

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

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

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

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

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

Calculate b to the power of 1 and get b.

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

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

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

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

$$\frac{a^{6}}{\left(bc^{2}\right)^{2}}$$

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

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

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

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