Solve (6(6)^(2)\times(3)^(2)((3)^(2)(5)^(2)(8)^(2)6)^(2))^(22) | 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

$${ \left(6 { 6 }^{ 2 } \times { 3 }^{ 2 } { \left( { 3 }^{ 2 } { 5 }^{ 2 } { 8 }^{ 2 } 6 \right) }^{ 2 } \right) }^{ 22 }$$

Evaluate

$36134529318775282606818895094703463124538180360914659476556189024031137336524649244852565750443214956264388499803201828720705887969815735341787309854228829294084057362623943273054724002307218477951221760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$

Solution Steps

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

$$\left(6^{3}\times 3^{2}\times \left(3^{2}\times 5^{2}\times 8^{2}\times 6\right)^{2}\right)^{22}$$

Calculate $6$ to the power of $3$ and get $216$.

$$\left(216\times 3^{2}\times \left(3^{2}\times 5^{2}\times 8^{2}\times 6\right)^{2}\right)^{22}$$

Calculate $3$ to the power of $2$ and get $9$.

$$\left(216\times 9\times \left(3^{2}\times 5^{2}\times 8^{2}\times 6\right)^{2}\right)^{22}$$

Multiply $216$ and $9$ to get $1944$.

$$\left(1944\times \left(3^{2}\times 5^{2}\times 8^{2}\times 6\right)^{2}\right)^{22}$$

Calculate $3$ to the power of $2$ and get $9$.

$$\left(1944\times \left(9\times 5^{2}\times 8^{2}\times 6\right)^{2}\right)^{22}$$

Calculate $5$ to the power of $2$ and get $25$.

$$\left(1944\times \left(9\times 25\times 8^{2}\times 6\right)^{2}\right)^{22}$$

Multiply $9$ and $25$ to get $225$.

$$\left(1944\times \left(225\times 8^{2}\times 6\right)^{2}\right)^{22}$$

Calculate $8$ to the power of $2$ and get $64$.

$$\left(1944\times \left(225\times 64\times 6\right)^{2}\right)^{22}$$

Multiply $225$ and $64$ to get $14400$.

$$\left(1944\times \left(14400\times 6\right)^{2}\right)^{22}$$

Multiply $14400$ and $6$ to get $86400$.

$$\left(1944\times 86400^{2}\right)^{22}$$

Calculate $86400$ to the power of $2$ and get $7464960000$.

$$\left(1944\times 7464960000\right)^{22}$$

Multiply $1944$ and $7464960000$ to get $14511882240000$.

$$14511882240000^{22}$$

Calculate $14511882240000$ to the power of $22$ and get $36134529318775282606818895094703463124538180360914659476556189024031137336524649244852565750443214956264388499803201828720705887969815735341787309854228829294084057362623943273054724002307218477951221760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$.

$$36134529318775282606818895094703463124538180360914659476556189024031137336524649244852565750443214956264388499803201828720705887969815735341787309854228829294084057362623943273054724002307218477951221760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$$

Factor

$2^{374}\times 3^{242}\times 5^{88}$