Solve (a^5b^4)^3

$$( a ^ { 5 } b ^ { 4 } ) ^ { 3 }$$

Evaluate

$$b^{12}a^{15}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(a^{5}b^{4}\right)^{3}$$

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

$$\left(a^{5}\right)^{3}\left(b^{4}\right)^{3}$$

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

$$a^{5\times 3}b^{4\times 3}$$

Multiply 5 times 3.

$$a^{15}b^{4\times 3}$$

Multiply 4 times 3.

$$a^{15}b^{12}$$

Expand

$$b^{12}a^{15}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(a^{5}b^{4}\right)^{3}$$

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

$$\left(a^{5}\right)^{3}\left(b^{4}\right)^{3}$$

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

$$a^{5\times 3}b^{4\times 3}$$

Multiply 5 times 3.

$$a^{15}b^{4\times 3}$$

Multiply 4 times 3.

$$a^{15}b^{12}$$