Solve 12a^5b^3*2b/4^8b^2b

$$\frac { 12 a ^ { 5 } b ^ { 3 } \times 2 b } { 4 ^ { 8 } b ^ { 2 } b }$$

Evaluate

$$\frac{3ba^{5}}{8192}$$

Solution Steps

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

$$\frac{12a^{5}b^{4}\times 2}{4^{8}b^{2}b}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{12a^{5}b^{4}\times 2}{4^{8}b^{3}}$$

Cancel out b^{3} in both numerator and denominator.

$$\frac{2\times 12ba^{5}}{4^{8}}$$

Multiply 2 and 12 to get 24.

$$\frac{24ba^{5}}{4^{8}}$$

Calculate 4 to the power of 8 and get 65536.

$$\frac{24ba^{5}}{65536}$$

Divide 24ba^{5} by 65536 to get \frac{3}{8192}ba^{5}.

$$\frac{3}{8192}ba^{5}$$

Differentiate w.r.t. a

$$\frac{15ba^{4}}{8192}$$