Solve {left(-a^3b^-1c^-3/4ab^3{c^-4}right)}^-3

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

Evaluate

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

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 -\frac{1}{64}.

$$\frac{c^{-3}a^{-6}}{-\frac{1}{64}b^{-12}}$$

Expand

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

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 -\frac{1}{64}.

$$\frac{c^{-3}a^{-6}}{-\frac{1}{64}b^{-12}}$$