Solve b^{3}quad11*(b^{4})^{2}*(a^{3})^{5}*(a^2b^3)^6*a^5div5

$$b ^ { 3 } \quad 11 \cdot ( b ^ { 4 } ) ^ { 2 } \times ( a ^ { 3 } ) ^ { 5 } \times ( a ^ { 2 } b ^ { 3 } ) ^ { 6 } \times a ^ { 5 } \div 5$$

Evaluate

$$\frac{11b^{29}a^{32}}{5}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{b^{3}\times 11b^{8}\left(a^{3}\right)^{5}\left(a^{2}b^{3}\right)^{6}a^{5}}{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{b^{3}\times 11b^{8}a^{15}\left(a^{2}b^{3}\right)^{6}a^{5}}{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\frac{b^{11}\times 11a^{15}\left(a^{2}b^{3}\right)^{6}a^{5}}{5}$$

To multiply powers of the same base, add their exponents. Add 15 and 5 to get 20.

$$\frac{b^{11}\times 11a^{20}\left(a^{2}b^{3}\right)^{6}}{5}$$

Expand \left(a^{2}b^{3}\right)^{6}.

$$\frac{b^{11}\times 11a^{20}\left(a^{2}\right)^{6}\left(b^{3}\right)^{6}}{5}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{b^{11}\times 11a^{20}a^{12}\left(b^{3}\right)^{6}}{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{b^{11}\times 11a^{20}a^{12}b^{18}}{5}$$

To multiply powers of the same base, add their exponents. Add 20 and 12 to get 32.

$$\frac{b^{11}\times 11a^{32}b^{18}}{5}$$

To multiply powers of the same base, add their exponents. Add 11 and 18 to get 29.

$$\frac{b^{29}\times 11a^{32}}{5}$$

Expand

$$\frac{11b^{29}a^{32}}{5}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{b^{3}\times 11b^{8}\left(a^{3}\right)^{5}\left(a^{2}b^{3}\right)^{6}a^{5}}{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{b^{3}\times 11b^{8}a^{15}\left(a^{2}b^{3}\right)^{6}a^{5}}{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\frac{b^{11}\times 11a^{15}\left(a^{2}b^{3}\right)^{6}a^{5}}{5}$$

To multiply powers of the same base, add their exponents. Add 15 and 5 to get 20.

$$\frac{b^{11}\times 11a^{20}\left(a^{2}b^{3}\right)^{6}}{5}$$

Expand \left(a^{2}b^{3}\right)^{6}.

$$\frac{b^{11}\times 11a^{20}\left(a^{2}\right)^{6}\left(b^{3}\right)^{6}}{5}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{b^{11}\times 11a^{20}a^{12}\left(b^{3}\right)^{6}}{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{b^{11}\times 11a^{20}a^{12}b^{18}}{5}$$

To multiply powers of the same base, add their exponents. Add 20 and 12 to get 32.

$$\frac{b^{11}\times 11a^{32}b^{18}}{5}$$

To multiply powers of the same base, add their exponents. Add 11 and 18 to get 29.

$$\frac{b^{29}\times 11a^{32}}{5}$$