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

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

Evaluate

$$-\frac{c^{3}a^{6}}{64b^{12}}$$

Short Solution Steps

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

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

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

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

Calculate c to the power of 1 and get c.

$$\left(\frac{c\left(-a^{3}\right)}{4ab^{4}}\right)^{3}$$

Factor the expressions that are not already factored in \frac{c\left(-a^{3}\right)}{4ab^{4}}.

$$\left(\frac{-ca^{3}}{4ab^{4}}\right)^{3}$$

Cancel out a in both numerator and denominator.

$$\left(\frac{-ca^{2}}{4b^{4}}\right)^{3}$$

Cancel out -1 in both numerator and denominator.

$$\left(\frac{ca^{2}}{-4b^{4}}\right)^{3}$$

To raise \frac{ca^{2}}{-4b^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(ca^{2}\right)^{3}}{\left(-4b^{4}\right)^{3}}$$

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

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

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

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

Expand \left(-4b^{4}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{c^{3}a^{6}}{\left(-4\right)^{3}b^{12}}$$

Calculate -4 to the power of 3 and get -64.

$$\frac{c^{3}a^{6}}{-64b^{12}}$$

Expand

$$-\frac{c^{3}a^{6}}{64b^{12}}$$

Short Solution Steps

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

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

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

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

Calculate c to the power of 1 and get c.

$$\left(\frac{c\left(-a^{3}\right)}{4ab^{4}}\right)^{3}$$

Factor the expressions that are not already factored in \frac{c\left(-a^{3}\right)}{4ab^{4}}.

$$\left(\frac{-ca^{3}}{4ab^{4}}\right)^{3}$$

Cancel out a in both numerator and denominator.

$$\left(\frac{-ca^{2}}{4b^{4}}\right)^{3}$$

Cancel out -1 in both numerator and denominator.

$$\left(\frac{ca^{2}}{-4b^{4}}\right)^{3}$$

To raise \frac{ca^{2}}{-4b^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(ca^{2}\right)^{3}}{\left(-4b^{4}\right)^{3}}$$

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

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

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

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

Expand \left(-4b^{4}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{c^{3}a^{6}}{\left(-4\right)^{3}b^{12}}$$

Calculate -4 to the power of 3 and get -64.

$$\frac{c^{3}a^{6}}{-64b^{12}}$$