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

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

Evaluate

$$8b^{6}a^{12}$$

Solution Steps

Cancel out 2b^{4} in both numerator and denominator.

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

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

$$\left(\frac{1}{2b^{2}a^{4}}\right)^{-3}$$

To raise \frac{1}{2b^{2}a^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-3}}{\left(2b^{2}a^{4}\right)^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{1}{\left(2b^{2}a^{4}\right)^{-3}}$$

Expand \left(2b^{2}a^{4}\right)^{-3}.

$$\frac{1}{2^{-3}\left(b^{2}\right)^{-3}\left(a^{4}\right)^{-3}}$$

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

$$\frac{1}{2^{-3}b^{-6}\left(a^{4}\right)^{-3}}$$

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

$$\frac{1}{2^{-3}b^{-6}a^{-12}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{1}{\frac{1}{8}b^{-6}a^{-12}}$$

Expand

$$8b^{6}a^{12}$$

Solution Steps

Cancel out 2b^{4} in both numerator and denominator.

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

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

$$\left(\frac{1}{2b^{2}a^{4}}\right)^{-3}$$

To raise \frac{1}{2b^{2}a^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-3}}{\left(2b^{2}a^{4}\right)^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{1}{\left(2b^{2}a^{4}\right)^{-3}}$$

Expand \left(2b^{2}a^{4}\right)^{-3}.

$$\frac{1}{2^{-3}\left(b^{2}\right)^{-3}\left(a^{4}\right)^{-3}}$$

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

$$\frac{1}{2^{-3}b^{-6}\left(a^{4}\right)^{-3}}$$

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

$$\frac{1}{2^{-3}b^{-6}a^{-12}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{1}{\frac{1}{8}b^{-6}a^{-12}}$$