Solve (b^6c^2)^9

$$( b ^ { 6 } c ^ { 2 } ) ^ { 9 }$$

Evaluate

$$c^{18}b^{54}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(b^{6}c^{2}\right)^{9}$$

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

$$\left(b^{6}\right)^{9}\left(c^{2}\right)^{9}$$

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

$$b^{6\times 9}c^{2\times 9}$$

Multiply 6 times 9.

$$b^{54}c^{2\times 9}$$

Multiply 2 times 9.

$$b^{54}c^{18}$$

Expand

$$c^{18}b^{54}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(b^{6}c^{2}\right)^{9}$$

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

$$\left(b^{6}\right)^{9}\left(c^{2}\right)^{9}$$

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

$$b^{6\times 9}c^{2\times 9}$$

Multiply 6 times 9.

$$b^{54}c^{2\times 9}$$

Multiply 2 times 9.

$$b^{54}c^{18}$$