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

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

Evaluate

$$\frac{a^{12}}{27b^{9}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -3.

$$\frac{1}{27}\left(a^{-4}\right)^{-3}\left(b^{3}\right)^{-3}$$

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

$$\frac{1}{27}a^{-4\left(-3\right)}b^{3\left(-3\right)}$$

Multiply -4 times -3.

$$\frac{1}{27}a^{12}b^{3\left(-3\right)}$$

Multiply 3 times -3.

$$\frac{1}{27}a^{12}\times \frac{1}{b^{9}}$$

Expand

$$\frac{a^{12}}{27b^{9}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -3.

$$\frac{1}{27}\left(a^{-4}\right)^{-3}\left(b^{3}\right)^{-3}$$

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

$$\frac{1}{27}a^{-4\left(-3\right)}b^{3\left(-3\right)}$$

Multiply -4 times -3.

$$\frac{1}{27}a^{12}b^{3\left(-3\right)}$$

Multiply 3 times -3.

$$\frac{1}{27}a^{12}\times \frac{1}{b^{9}}$$