Solve 54a^{6}b^5c^2diva^2c/bdivsqrt[3]{33/8}c^3

$$54 a ^ { 6 } b ^ { 5 } c ^ { 2 } \div \frac { a ^ { 2 } c } { b } \div \sqrt[ 3 ] { 3 \frac { 3 } { 8 } } c ^ { 3 }$$

Evaluate

$$36b^{6}\left(ac\right)^{4}$$

Solution Steps

Divide 54a^{6}b^{5}c^{2} by \frac{a^{2}c}{b} by multiplying 54a^{6}b^{5}c^{2} by the reciprocal of \frac{a^{2}c}{b}.

$$\frac{\frac{54a^{6}b^{5}c^{2}b}{a^{2}c}}{\sqrt[3]{\frac{3\times 8+3}{8}}}c^{3}$$

Cancel out ca^{2} in both numerator and denominator.

$$\frac{54bca^{4}b^{5}}{\sqrt[3]{\frac{3\times 8+3}{8}}}c^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{54b^{6}ca^{4}}{\sqrt[3]{\frac{3\times 8+3}{8}}}c^{3}$$

Multiply 3 and 8 to get 24.

$$\frac{54b^{6}ca^{4}}{\sqrt[3]{\frac{24+3}{8}}}c^{3}$$

Add 24 and 3 to get 27.

$$\frac{54b^{6}ca^{4}}{\sqrt[3]{\frac{27}{8}}}c^{3}$$

Calculate \sqrt[3]{\frac{27}{8}} and get \frac{3}{2}.

$$\frac{54b^{6}ca^{4}}{\frac{3}{2}}c^{3}$$

Divide 54b^{6}ca^{4} by \frac{3}{2} by multiplying 54b^{6}ca^{4} by the reciprocal of \frac{3}{2}.

$$\frac{54b^{6}ca^{4}\times 2}{3}c^{3}$$

Multiply 54 and 2 to get 108.

$$\frac{108b^{6}ca^{4}}{3}c^{3}$$

Divide 108b^{6}ca^{4} by 3 to get 36b^{6}ca^{4}.

$$36b^{6}ca^{4}c^{3}$$

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

$$36b^{6}c^{4}a^{4}$$

Differentiate w.r.t. a

$$144a^{3}c^{4}b^{6}$$