Solve (1)(-3a^2b^3)^4

$$( 1 ) ( - 3 a ^ { 2 } b ^ { 3 } ) ^ { 4 }$$

Evaluate

$$81a^{8}b^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -3 to the power 4.

$$81\left(a^{2}\right)^{4}\left(b^{3}\right)^{4}$$

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

$$81a^{2\times 4}b^{3\times 4}$$

Multiply 2 times 4.

$$81a^{8}b^{3\times 4}$$

Multiply 3 times 4.

$$81a^{8}b^{12}$$

Expand

$$81a^{8}b^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -3 to the power 4.

$$81\left(a^{2}\right)^{4}\left(b^{3}\right)^{4}$$

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

$$81a^{2\times 4}b^{3\times 4}$$

Multiply 2 times 4.

$$81a^{8}b^{3\times 4}$$

Multiply 3 times 4.

$$81a^{8}b^{12}$$