Solve (a^-3b/ab^4)^-4

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

Evaluate

$$b^{12}a^{16}$$

Solution Steps

Cancel out b in both numerator and denominator.

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

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

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

To raise \frac{1}{b^{3}a^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 1 to the power of -4 and get 1.

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

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

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

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

$$\frac{1}{b^{-12}\left(a^{4}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -4 to get -16.

$$\frac{1}{b^{-12}a^{-16}}$$

Expand

$$b^{12}a^{16}$$

Solution Steps

Cancel out b in both numerator and denominator.

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

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

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

To raise \frac{1}{b^{3}a^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 1 to the power of -4 and get 1.

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

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

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

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

$$\frac{1}{b^{-12}\left(a^{4}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -4 to get -16.

$$\frac{1}{b^{-12}a^{-16}}$$