Solve (4a^2b^3)^3=

$$( 4 a ^ { 2 } b ^ { 3 } ) ^ { 3 } =$$

Evaluate

$$64a^{6}b^{9}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 3.

$$64\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}$$

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

$$64a^{2\times 3}b^{3\times 3}$$

Multiply 2 times 3.

$$64a^{6}b^{3\times 3}$$

Multiply 3 times 3.

$$64a^{6}b^{9}$$

Expand

$$64a^{6}b^{9}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 3.

$$64\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}$$

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

$$64a^{2\times 3}b^{3\times 3}$$

Multiply 2 times 3.

$$64a^{6}b^{3\times 3}$$

Multiply 3 times 3.

$$64a^{6}b^{9}$$