Solve [(12a^4b^2)^-3]=

$$[ ( 12 a ^ { 4 } b ^ { 2 } ) ^ { - 3 } ] =$$

Evaluate

$$\frac{1}{1728b^{6}a^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(12a^{4}b^{2}\right)^{-3}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$12^{-3}\left(a^{4}\right)^{-3}\left(b^{2}\right)^{-3}$$

Raise 12 to the power -3.

$$\frac{1}{1728}\left(a^{4}\right)^{-3}\left(b^{2}\right)^{-3}$$

To raise a power to another power, multiply the exponents.

$$\frac{1}{1728}a^{4\left(-3\right)}b^{2\left(-3\right)}$$

Multiply 4 times -3.

$$\frac{1}{1728}\times \frac{1}{a^{12}}b^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{1728}\times \frac{1}{a^{12}}\times \frac{1}{b^{6}}$$

Expand

$$\frac{1}{1728b^{6}a^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(12a^{4}b^{2}\right)^{-3}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$12^{-3}\left(a^{4}\right)^{-3}\left(b^{2}\right)^{-3}$$

Raise 12 to the power -3.

$$\frac{1}{1728}\left(a^{4}\right)^{-3}\left(b^{2}\right)^{-3}$$

To raise a power to another power, multiply the exponents.

$$\frac{1}{1728}a^{4\left(-3\right)}b^{2\left(-3\right)}$$

Multiply 4 times -3.

$$\frac{1}{1728}\times \frac{1}{a^{12}}b^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{1728}\times \frac{1}{a^{12}}\times \frac{1}{b^{6}}$$