Solve (a*b)^4*(a^2*b^3)^3

$$( a \cdot b ) ^ { 4 } \cdot ( a ^ { 2 } \cdot b ^ { 3 } ) ^ { 3 }$$

Evaluate

$$a^{10}b^{13}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(a^{1}b^{1}\right)^{4}\left(a^{2}b^{3}\right)^{3}$$

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

$$\left(a^{1}\right)^{4}\left(b^{1}\right)^{4}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}$$

Use the Commutative Property of Multiplication.

$$\left(a^{1}\right)^{4}\left(a^{2}\right)^{3}\left(b^{1}\right)^{4}\left(b^{3}\right)^{3}$$

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

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

Multiply 2 times 3.

$$a^{4}a^{6}b^{4}b^{3\times 3}$$

Multiply 3 times 3.

$$a^{4}a^{6}b^{4}b^{9}$$

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

$$a^{4+6}b^{4+9}$$

Add the exponents 4 and 6.

$$a^{10}b^{4+9}$$

Add the exponents 4 and 9.

$$a^{10}b^{13}$$

Expand

$$a^{10}b^{13}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(a^{1}b^{1}\right)^{4}\left(a^{2}b^{3}\right)^{3}$$

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

$$\left(a^{1}\right)^{4}\left(b^{1}\right)^{4}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}$$

Use the Commutative Property of Multiplication.

$$\left(a^{1}\right)^{4}\left(a^{2}\right)^{3}\left(b^{1}\right)^{4}\left(b^{3}\right)^{3}$$

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

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

Multiply 2 times 3.

$$a^{4}a^{6}b^{4}b^{3\times 3}$$

Multiply 3 times 3.

$$a^{4}a^{6}b^{4}b^{9}$$

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

$$a^{4+6}b^{4+9}$$

Add the exponents 4 and 6.

$$a^{10}b^{4+9}$$

Add the exponents 4 and 9.

$$a^{10}b^{13}$$