Solve (4a^5b^6)^2

$$( 4 a ^ { 5 } b ^ { 6 } ) ^ { 2 }$$

Evaluate

$$16a^{10}b^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4a^{5}b^{6}\right)^{2}$$

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

$$4^{2}\left(a^{5}\right)^{2}\left(b^{6}\right)^{2}$$

Raise 4 to the power 2.

$$16\left(a^{5}\right)^{2}\left(b^{6}\right)^{2}$$

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

$$16a^{5\times 2}b^{6\times 2}$$

Multiply 5 times 2.

$$16a^{10}b^{6\times 2}$$

Multiply 6 times 2.

$$16a^{10}b^{12}$$

Expand

$$16a^{10}b^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4a^{5}b^{6}\right)^{2}$$

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

$$4^{2}\left(a^{5}\right)^{2}\left(b^{6}\right)^{2}$$

Raise 4 to the power 2.

$$16\left(a^{5}\right)^{2}\left(b^{6}\right)^{2}$$

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

$$16a^{5\times 2}b^{6\times 2}$$

Multiply 5 times 2.

$$16a^{10}b^{6\times 2}$$

Multiply 6 times 2.

$$16a^{10}b^{12}$$