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

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

Evaluate

$$\frac{b^{9}}{a^{21}}$$

Solution Steps

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{a^{-12}b^{12}}{a^{9}b^{3}}$$

Cancel out b^{3} in both numerator and denominator.

$$\frac{a^{-12}b^{9}}{a^{9}}$$

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

$$\frac{b^{9}}{a^{21}}$$

Expand

$$\frac{b^{9}}{a^{21}}$$

Solution Steps

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{a^{-12}b^{12}}{a^{9}b^{3}}$$

Cancel out b^{3} in both numerator and denominator.

$$\frac{a^{-12}b^{9}}{a^{9}}$$

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

$$\frac{b^{9}}{a^{21}}$$