Solve 2a^4b*3ab^3div6(ab)^4

$$2 a ^ { 4 } b \times 3 a b ^ { 3 } \div 6 ( a b ) ^ { 4 }$$

Evaluate

$$b^{8}a^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{2a^{5}b\times 3b^{3}}{6}\left(ab\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{2a^{5}b^{4}\times 3}{6}\left(ab\right)^{4}$$

Multiply 2 and 3 to get 6.

$$\frac{6a^{5}b^{4}}{6}\left(ab\right)^{4}$$

Cancel out 6 and 6.

$$a^{5}b^{4}\left(ab\right)^{4}$$

Expand \left(ab\right)^{4}.

$$a^{5}b^{4}a^{4}b^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

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

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$a^{9}b^{8}$$

Expand

$$b^{8}a^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{2a^{5}b\times 3b^{3}}{6}\left(ab\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{2a^{5}b^{4}\times 3}{6}\left(ab\right)^{4}$$

Multiply 2 and 3 to get 6.

$$\frac{6a^{5}b^{4}}{6}\left(ab\right)^{4}$$

Cancel out 6 and 6.

$$a^{5}b^{4}\left(ab\right)^{4}$$

Expand \left(ab\right)^{4}.

$$a^{5}b^{4}a^{4}b^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

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

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$a^{9}b^{8}$$