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

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

Evaluate

$$b^{5}a^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

$$a^{3\times 3}\times \frac{1}{a}b^{2\times 3}\times \frac{1}{b}$$

Multiply 3 times 3.

$$a^{9}\times \frac{1}{a}b^{2\times 3}\times \frac{1}{b}$$

Multiply 2 times 3.

$$a^{9}\times \frac{1}{a}b^{6}\times \frac{1}{b}$$

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

$$a^{9-1}b^{6-1}$$

Add the exponents 9 and -1.

$$a^{8}b^{6-1}$$

Add the exponents 6 and -1.

$$a^{8}b^{5}$$

Expand

$$b^{5}a^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

$$a^{3\times 3}\times \frac{1}{a}b^{2\times 3}\times \frac{1}{b}$$

Multiply 3 times 3.

$$a^{9}\times \frac{1}{a}b^{2\times 3}\times \frac{1}{b}$$

Multiply 2 times 3.

$$a^{9}\times \frac{1}{a}b^{6}\times \frac{1}{b}$$

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

$$a^{9-1}b^{6-1}$$

Add the exponents 9 and -1.

$$a^{8}b^{6-1}$$

Add the exponents 6 and -1.

$$a^{8}b^{5}$$