Solve (ab^2)^3div(ab^2)

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

Evaluate

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times 3.

$$a^{3}\times \frac{1}{a}b^{6}b^{2\left(-1\right)}$$

Multiply 2 times -1.

$$a^{3}\times \frac{1}{a}b^{6}b^{-2}$$

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

$$a^{3-1}b^{6-2}$$

Add the exponents 3 and -1.

$$a^{2}b^{6-2}$$

Add the exponents 6 and -2.

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

Expand

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times 3.

$$a^{3}\times \frac{1}{a}b^{6}b^{2\left(-1\right)}$$

Multiply 2 times -1.

$$a^{3}\times \frac{1}{a}b^{6}b^{-2}$$

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

$$a^{3-1}b^{6-2}$$

Add the exponents 3 and -1.

$$a^{2}b^{6-2}$$

Add the exponents 6 and -2.

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