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

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

Evaluate

$$a^{7}b^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times 2.

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

Multiply 2 times 3.

$$a^{4}a^{3}b^{2}b^{6}$$

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

$$a^{4+3}b^{2+6}$$

Add the exponents 4 and 3.

$$a^{7}b^{2+6}$$

Add the exponents 2 and 6.

$$a^{7}b^{8}$$

Expand

$$a^{7}b^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times 2.

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

Multiply 2 times 3.

$$a^{4}a^{3}b^{2}b^{6}$$

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

$$a^{4+3}b^{2+6}$$

Add the exponents 4 and 3.

$$a^{7}b^{2+6}$$

Add the exponents 2 and 6.

$$a^{7}b^{8}$$