Solve (ab)^2*(ab)^3

$$( a b ) ^ { 2 } \times ( a b ) ^ { 3 }$$

Evaluate

$$\left(ab\right)^{5}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(a^{1}b^{1}\right)^{2}\left(a^{1}b^{1}\right)^{3}$$

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

$$\left(a^{1}\right)^{2}\left(b^{1}\right)^{2}\left(a^{1}\right)^{3}\left(b^{1}\right)^{3}$$

Use the Commutative Property of Multiplication.

$$\left(a^{1}\right)^{2}\left(a^{1}\right)^{3}\left(b^{1}\right)^{2}\left(b^{1}\right)^{3}$$

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

$$a^{2}a^{3}b^{2}b^{3}$$

To multiply powers of the same base, add their exponents.

$$a^{2+3}b^{2+3}$$

Add the exponents 2 and 3.

$$a^{5}b^{2+3}$$

Add the exponents 2 and 3.

$$a^{5}b^{5}$$

Expand

$$\left(ab\right)^{5}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(a^{1}b^{1}\right)^{2}\left(a^{1}b^{1}\right)^{3}$$

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

$$\left(a^{1}\right)^{2}\left(b^{1}\right)^{2}\left(a^{1}\right)^{3}\left(b^{1}\right)^{3}$$

Use the Commutative Property of Multiplication.

$$\left(a^{1}\right)^{2}\left(a^{1}\right)^{3}\left(b^{1}\right)^{2}\left(b^{1}\right)^{3}$$

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

$$a^{2}a^{3}b^{2}b^{3}$$

To multiply powers of the same base, add their exponents.

$$a^{2+3}b^{2+3}$$

Add the exponents 2 and 3.

$$a^{5}b^{2+3}$$

Add the exponents 2 and 3.

$$a^{5}b^{5}$$