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

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

Evaluate

$$\frac{b^{16}}{c^{4}a^{10}}$$

Solution Steps

Cancel out c in both numerator and denominator.

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

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

$$\left(\frac{a^{-4}b^{8}}{ac^{2}}\right)^{2}$$

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

$$\left(\frac{b^{8}}{c^{2}a^{5}}\right)^{2}$$

To raise \frac{b^{8}}{c^{2}a^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{8}\right)^{2}}{\left(c^{2}a^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{b^{16}}{\left(c^{2}a^{5}\right)^{2}}$$

Expand \left(c^{2}a^{5}\right)^{2}.

$$\frac{b^{16}}{\left(c^{2}\right)^{2}\left(a^{5}\right)^{2}}$$

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

$$\frac{b^{16}}{c^{4}\left(a^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{b^{16}}{c^{4}a^{10}}$$

Expand

$$\frac{b^{16}}{c^{4}a^{10}}$$

Solution Steps

Cancel out c in both numerator and denominator.

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

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

$$\left(\frac{a^{-4}b^{8}}{ac^{2}}\right)^{2}$$

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

$$\left(\frac{b^{8}}{c^{2}a^{5}}\right)^{2}$$

To raise \frac{b^{8}}{c^{2}a^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{8}\right)^{2}}{\left(c^{2}a^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{b^{16}}{\left(c^{2}a^{5}\right)^{2}}$$

Expand \left(c^{2}a^{5}\right)^{2}.

$$\frac{b^{16}}{\left(c^{2}\right)^{2}\left(a^{5}\right)^{2}}$$

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

$$\frac{b^{16}}{c^{4}\left(a^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{b^{16}}{c^{4}a^{10}}$$