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

$$( 5 a ^ { 2 } b ^ { 3 } ) ^ { 5 }$$

Evaluate

$$3125a^{10}b^{15}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 5 to the power 5.

$$3125\left(a^{2}\right)^{5}\left(b^{3}\right)^{5}$$

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

$$3125a^{2\times 5}b^{3\times 5}$$

Multiply 2 times 5.

$$3125a^{10}b^{3\times 5}$$

Multiply 3 times 5.

$$3125a^{10}b^{15}$$

Expand

$$3125a^{10}b^{15}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 5 to the power 5.

$$3125\left(a^{2}\right)^{5}\left(b^{3}\right)^{5}$$

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

$$3125a^{2\times 5}b^{3\times 5}$$

Multiply 2 times 5.

$$3125a^{10}b^{3\times 5}$$

Multiply 3 times 5.

$$3125a^{10}b^{15}$$