Solve left(5a^2b^3right)^3

$${ \left(5 { a }^{ 2 } { b }^{ 3 } \right) }^{ 3 }$$

Evaluate

$$125a^{6}b^{9}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5a^{2}b^{3}\right)^{3}$$

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

$$5^{3}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}$$

Raise 5 to the power 3.

$$125\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}$$

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

$$125a^{2\times 3}b^{3\times 3}$$

Multiply 2 times 3.

$$125a^{6}b^{3\times 3}$$

Multiply 3 times 3.

$$125a^{6}b^{9}$$

Expand

$$125a^{6}b^{9}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5a^{2}b^{3}\right)^{3}$$

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

$$5^{3}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}$$

Raise 5 to the power 3.

$$125\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}$$

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

$$125a^{2\times 3}b^{3\times 3}$$

Multiply 2 times 3.

$$125a^{6}b^{3\times 3}$$

Multiply 3 times 3.

$$125a^{6}b^{9}$$