Solve (2a^3b^-2)^3

$$( 2 a ^ { 3 } b ^ { - 2 } ) ^ { 3 }$$

Evaluate

$$\frac{8a^{9}}{b^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power 3.

$$8\left(a^{3}\right)^{3}\left(b^{-2}\right)^{3}$$

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

$$8a^{3\times 3}b^{-2\times 3}$$

Multiply 3 times 3.

$$8a^{9}b^{-2\times 3}$$

Multiply -2 times 3.

$$8a^{9}\times \frac{1}{b^{6}}$$

Expand

$$\frac{8a^{9}}{b^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power 3.

$$8\left(a^{3}\right)^{3}\left(b^{-2}\right)^{3}$$

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

$$8a^{3\times 3}b^{-2\times 3}$$

Multiply 3 times 3.

$$8a^{9}b^{-2\times 3}$$

Multiply -2 times 3.

$$8a^{9}\times \frac{1}{b^{6}}$$