Solve frac{(a^{3}b^4)^3}{a^3b^8}

$$\frac { ( a ^ { 3 } b ^ { 4 } ) ^ { 3 } } { a ^ { 3 } b ^ { 8 } }$$

Evaluate

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(a^{3}b^{4}\right)^{3}\times \frac{1}{a^{3}b^{8}}$$

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

$$\left(a^{3}\right)^{3}\left(b^{4}\right)^{3}\times \frac{1}{a^{3}}\times \frac{1}{b^{8}}$$

Use the Commutative Property of Multiplication.

$$\left(a^{3}\right)^{3}\times \frac{1}{a^{3}}\left(b^{4}\right)^{3}\times \frac{1}{b^{8}}$$

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

$$a^{3\times 3}a^{3\left(-1\right)}b^{4\times 3}b^{8\left(-1\right)}$$

Multiply 3 times 3.

$$a^{9}a^{3\left(-1\right)}b^{4\times 3}b^{8\left(-1\right)}$$

Multiply 3 times -1.

$$a^{9}a^{-3}b^{4\times 3}b^{8\left(-1\right)}$$

Multiply 4 times 3.

$$a^{9}a^{-3}b^{12}b^{8\left(-1\right)}$$

Multiply 8 times -1.

$$a^{9}a^{-3}b^{12}b^{-8}$$

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

$$a^{9-3}b^{12-8}$$

Add the exponents 9 and -3.

$$a^{6}b^{12-8}$$

Add the exponents 12 and -8.

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

Expand

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(a^{3}b^{4}\right)^{3}\times \frac{1}{a^{3}b^{8}}$$

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

$$\left(a^{3}\right)^{3}\left(b^{4}\right)^{3}\times \frac{1}{a^{3}}\times \frac{1}{b^{8}}$$

Use the Commutative Property of Multiplication.

$$\left(a^{3}\right)^{3}\times \frac{1}{a^{3}}\left(b^{4}\right)^{3}\times \frac{1}{b^{8}}$$

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

$$a^{3\times 3}a^{3\left(-1\right)}b^{4\times 3}b^{8\left(-1\right)}$$

Multiply 3 times 3.

$$a^{9}a^{3\left(-1\right)}b^{4\times 3}b^{8\left(-1\right)}$$

Multiply 3 times -1.

$$a^{9}a^{-3}b^{4\times 3}b^{8\left(-1\right)}$$

Multiply 4 times 3.

$$a^{9}a^{-3}b^{12}b^{8\left(-1\right)}$$

Multiply 8 times -1.

$$a^{9}a^{-3}b^{12}b^{-8}$$

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

$$a^{9-3}b^{12-8}$$

Add the exponents 9 and -3.

$$a^{6}b^{12-8}$$

Add the exponents 12 and -8.

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