Solve (4/5) ^ 5 * (4/15) ^ 6 + (3/4) ^ 2 | 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

$$(\frac{4}{5})^{5}\times(\frac{4}{15})^{6}+(\frac{3}{4})^{2}$$

Evaluate

$\frac{320428436989}{569531250000}\approx 0.562617832$

Solution Steps

Calculate $\frac{4}{5}$ to the power of $5$ and get $\frac{1024}{3125}$.

$$\frac{1024}{3125}\times \left(\frac{4}{15}\right)^{6}+\left(\frac{3}{4}\right)^{2}$$

Calculate $\frac{4}{15}$ to the power of $6$ and get $\frac{4096}{11390625}$.

$$\frac{1024}{3125}\times \frac{4096}{11390625}+\left(\frac{3}{4}\right)^{2}$$

Multiply $\frac{1024}{3125}$ times $\frac{4096}{11390625}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1024\times 4096}{3125\times 11390625}+\left(\frac{3}{4}\right)^{2}$$

Do the multiplications in the fraction $\frac{1024\times 4096}{3125\times 11390625}$.

$$\frac{4194304}{35595703125}+\left(\frac{3}{4}\right)^{2}$$

Calculate $\frac{3}{4}$ to the power of $2$ and get $\frac{9}{16}$.

$$\frac{4194304}{35595703125}+\frac{9}{16}$$

Least common multiple of $35595703125$ and $16$ is $569531250000$. Convert $\frac{4194304}{35595703125}$ and $\frac{9}{16}$ to fractions with denominator $569531250000$.

$$\frac{67108864}{569531250000}+\frac{320361328125}{569531250000}$$

Since $\frac{67108864}{569531250000}$ and $\frac{320361328125}{569531250000}$ have the same denominator, add them by adding their numerators.

$$\frac{67108864+320361328125}{569531250000}$$

Add $67108864$ and $320361328125$ to get $320428436989$.

$$\frac{320428436989}{569531250000}$$

Factor

$\frac{42407 \cdot 7556027}{2 ^ {4} \cdot 3 ^ {6} \cdot 5 ^ {11}} = 0.5626178317502332$