Solve left(a^2bright)^3*{left(a^2b^4right)}^-1

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

Evaluate

$$\frac{a^{4}}{b}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times 3.

$$a^{6}a^{2\left(-1\right)}b^{3}b^{4\left(-1\right)}$$

Multiply 2 times -1.

$$a^{6}a^{-2}b^{3}b^{4\left(-1\right)}$$

Multiply 4 times -1.

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

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

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

Add the exponents 6 and -2.

$$a^{4}b^{3-4}$$

Add the exponents 3 and -4.

$$a^{4}\times \frac{1}{b}$$

Expand

$$\frac{a^{4}}{b}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times 3.

$$a^{6}a^{2\left(-1\right)}b^{3}b^{4\left(-1\right)}$$

Multiply 2 times -1.

$$a^{6}a^{-2}b^{3}b^{4\left(-1\right)}$$

Multiply 4 times -1.

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

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

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

Add the exponents 6 and -2.

$$a^{4}b^{3-4}$$

Add the exponents 3 and -4.

$$a^{4}\times \frac{1}{b}$$