Solve (5)/(9)DELOS(8)/(40)DELOS(5)/(7)DELDOBLEDE5 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{ 5 }{ 9 } DELOS \frac{ 8 }{ 40 } DELOS \frac{ 5 }{ 7 } DELDOBLEDE5$$

Evaluate

$\frac{5BE_{5}S^{2}O^{3}D^{5}\left(EL\right)^{4}}{63}$

Solution Steps

Multiply $D$ and $D$ to get $D^{2}$.

$$\frac{5}{9}D^{2}ELOS\times \frac{8}{40}ELOS\times \frac{5}{7}DELDOBLEDE_{5}$$

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

$$\frac{5}{9}D^{3}ELOS\times \frac{8}{40}ELOS\times \frac{5}{7}ELDOBLEDE_{5}$$

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

$$\frac{5}{9}D^{4}ELOS\times \frac{8}{40}ELOS\times \frac{5}{7}ELOBLEDE_{5}$$

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

$$\frac{5}{9}D^{5}ELOS\times \frac{8}{40}ELOS\times \frac{5}{7}ELOBLEE_{5}$$

Multiply $E$ and $E$ to get $E^{2}$.

$$\frac{5}{9}D^{5}E^{2}LOS\times \frac{8}{40}LOS\times \frac{5}{7}ELOBLEE_{5}$$

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

$$\frac{5}{9}D^{5}E^{3}LOS\times \frac{8}{40}LOS\times \frac{5}{7}LOBLEE_{5}$$

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

$$\frac{5}{9}D^{5}E^{4}LOS\times \frac{8}{40}LOS\times \frac{5}{7}LOBLE_{5}$$

Multiply $L$ and $L$ to get $L^{2}$.

$$\frac{5}{9}D^{5}E^{4}L^{2}OS\times \frac{8}{40}OS\times \frac{5}{7}LOBLE_{5}$$

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

$$\frac{5}{9}D^{5}E^{4}L^{3}OS\times \frac{8}{40}OS\times \frac{5}{7}OBLE_{5}$$

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

$$\frac{5}{9}D^{5}E^{4}L^{4}OS\times \frac{8}{40}OS\times \frac{5}{7}OBE_{5}$$

Multiply $O$ and $O$ to get $O^{2}$.

$$\frac{5}{9}D^{5}E^{4}L^{4}O^{2}S\times \frac{8}{40}S\times \frac{5}{7}OBE_{5}$$

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

$$\frac{5}{9}D^{5}E^{4}L^{4}O^{3}S\times \frac{8}{40}S\times \frac{5}{7}BE_{5}$$

Multiply $S$ and $S$ to get $S^{2}$.

$$\frac{5}{9}D^{5}E^{4}L^{4}O^{3}S^{2}\times \frac{8}{40}\times \frac{5}{7}BE_{5}$$

Reduce the fraction $\frac{8}{40}$ to lowest terms by extracting and canceling out $8$.

$$\frac{5}{9}D^{5}E^{4}L^{4}O^{3}S^{2}\times \frac{1}{5}\times \frac{5}{7}BE_{5}$$

Multiply $\frac{5}{9}$ times $\frac{1}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 1}{9\times 5}D^{5}E^{4}L^{4}O^{3}S^{2}\times \frac{5}{7}BE_{5}$$

Cancel out $5$ in both numerator and denominator.

$$\frac{1}{9}D^{5}E^{4}L^{4}O^{3}S^{2}\times \frac{5}{7}BE_{5}$$

Multiply $\frac{1}{9}$ times $\frac{5}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{9\times 7}D^{5}E^{4}L^{4}O^{3}S^{2}BE_{5}$$

Do the multiplications in the fraction $\frac{1\times 5}{9\times 7}$.

$$\frac{5}{63}D^{5}E^{4}L^{4}O^{3}S^{2}BE_{5}$$

Differentiate w.r.t. B

$\frac{5E_{5}S^{2}O^{3}D^{5}\left(EL\right)^{4}}{63}$