Solve Simplify (2 ^ (1/3) * (27) ^ (1/3) * (60) ^ (1/2))/((180) ^ (1/2) * (4) ^ (- 1/3) * (9) ^ (1/4)) 523 | 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

$$\frac { 8 } { 18 } \times \frac { 28 \times 139 ^ { 13 } \times 100 ^ { 13 } } { 1800 ^ { 12 } \times ( 4 ) ^ { 13 } }$$

Evaluate

$\frac{1265407639332057004301289978325}{10917230603493005328384}\approx 115909215.925803152$

Solution Steps

Reduce the fraction $\frac{8}{18}$ to lowest terms by extracting and canceling out $2$.

$$\frac{4}{9}\times \frac{28\times 139^{13}\times 100^{13}}{1800^{12}\times 4^{13}}$$

Calculate $139$ to the power of $13$ and get $7230900796183182881721657019$.

$$\frac{4}{9}\times \frac{28\times 7230900796183182881721657019\times 100^{13}}{1800^{12}\times 4^{13}}$$

Multiply $28$ and $7230900796183182881721657019$ to get $202465222293129120688206396532$.

$$\frac{4}{9}\times \frac{202465222293129120688206396532\times 100^{13}}{1800^{12}\times 4^{13}}$$

Calculate $100$ to the power of $13$ and get $100000000000000000000000000$.

$$\frac{4}{9}\times \frac{202465222293129120688206396532\times 100000000000000000000000000}{1800^{12}\times 4^{13}}$$

Multiply $202465222293129120688206396532$ and $100000000000000000000000000$ to get $20246522229312912068820639653200000000000000000000000000$.

$$\frac{4}{9}\times \frac{20246522229312912068820639653200000000000000000000000000}{1800^{12}\times 4^{13}}$$

Calculate $1800$ to the power of $12$ and get $1156831381426176000000000000000000000000$.

$$\frac{4}{9}\times \frac{20246522229312912068820639653200000000000000000000000000}{1156831381426176000000000000000000000000\times 4^{13}}$$

Calculate $4$ to the power of $13$ and get $67108864$.

$$\frac{4}{9}\times \frac{20246522229312912068820639653200000000000000000000000000}{1156831381426176000000000000000000000000\times 67108864}$$

Multiply $1156831381426176000000000000000000000000$ and $67108864$ to get $77633639847061371224064000000000000000000000000$.

$$\frac{4}{9}\times \frac{20246522229312912068820639653200000000000000000000000000}{77633639847061371224064000000000000000000000000}$$

Reduce the fraction $\frac{20246522229312912068820639653200000000000000000000000000}{77633639847061371224064000000000000000000000000}$ to lowest terms by extracting and canceling out $16000000000000000000000000$.

$$\frac{4}{9}\times \frac{1265407639332057004301289978325}{4852102490441335701504}$$

Multiply $\frac{4}{9}$ times $\frac{1265407639332057004301289978325}{4852102490441335701504}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 1265407639332057004301289978325}{9\times 4852102490441335701504}$$

Do the multiplications in the fraction $\frac{4\times 1265407639332057004301289978325}{9\times 4852102490441335701504}$.

$$\frac{5061630557328228017205159913300}{43668922413972021313536}$$

Reduce the fraction $\frac{5061630557328228017205159913300}{43668922413972021313536}$ to lowest terms by extracting and canceling out $4$.

$$\frac{1265407639332057004301289978325}{10917230603493005328384}$$

Factor

$\frac{5 ^ {2} \cdot 7 \cdot 139 ^ {13}}{2 ^ {32} \cdot 3 ^ {26}} = 115909215\frac{1.0107206443991157 \times 10^{22}}{1.0917230603493004 \times 10^{22}} = 115909215.92580314$