Solve 7^13:7^11text{ede}2^-4.2^5?

$$7 ^ { 13 } : 7 ^ { 11 } \text { e de } 2 ^ { - 4 } .2 ^ { 5 } ?$$

Evaluate

$$\frac{49e^{2}d}{50000}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 11 from 13 to get 2.

$$7^{2}ede\times 2^{-4}\times 0.2^{5}$$

Multiply e and e to get e^{2}.

$$7^{2}e^{2}d\times 2^{-4}\times 0.2^{5}$$

Calculate 7 to the power of 2 and get 49.

$$49e^{2}d\times 2^{-4}\times 0.2^{5}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$49e^{2}d\times \frac{1}{16}\times 0.2^{5}$$

Multiply 49 and \frac{1}{16} to get \frac{49}{16}.

$$\frac{49}{16}e^{2}d\times 0.2^{5}$$

Calculate 0.2 to the power of 5 and get 0.00032.

$$\frac{49}{16}e^{2}d\times 0.00032$$

Multiply \frac{49}{16} and 0.00032 to get \frac{49}{50000}.

$$\frac{49}{50000}e^{2}d$$

Differentiate w.r.t. d

$$\frac{49e^{2}}{50000}$$