Solve Simplify 2 3 1 15 X | 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

$$\frac { 8 m + 15 } { 2 ^ { 2 } \times 3 ^ { 22 - 5 } \times 5 ^ { 2 + 5 } \times 6 ^ { 25 + 13 } \times 6 ^ { 311 } }$$

Evaluate

$\frac{m}{189499360549332809565562429660098168244572234392573468990529588435600328811311123986373057132900600855711244176180796613705848355142324259301684297675107186554064940719388667440630761710121561373988417214354418713831752656333549191670000028784675477278004124591765301560952750080000000}+\frac{1}{101066325626310831768299962485385689730438525009372516794949113832320175366032599459398963804213653789712663560629758193976452456075906271627564958760057166162167968383673955968336406245398166066127155847655689980710268083377892902224000015351826921214935533115608160832508133376000000}$

Solution Steps

Calculate $2$ to the power of $2$ and get $4$.

$$\frac{8m+15}{4\times 3^{22-5}\times 5^{2+5}\times 6^{25+13}\times 6^{311}}$$

Subtract $5$ from $22$ to get $17$.

$$\frac{8m+15}{4\times 3^{17}\times 5^{2+5}\times 6^{25+13}\times 6^{311}}$$

Calculate $3$ to the power of $17$ and get $129140163$.

$$\frac{8m+15}{4\times 129140163\times 5^{2+5}\times 6^{25+13}\times 6^{311}}$$

Multiply $4$ and $129140163$ to get $516560652$.

$$\frac{8m+15}{516560652\times 5^{2+5}\times 6^{25+13}\times 6^{311}}$$

Add $2$ and $5$ to get $7$.

$$\frac{8m+15}{516560652\times 5^{7}\times 6^{25+13}\times 6^{311}}$$

Calculate $5$ to the power of $7$ and get $78125$.

$$\frac{8m+15}{516560652\times 78125\times 6^{25+13}\times 6^{311}}$$

Multiply $516560652$ and $78125$ to get $40356300937500$.

$$\frac{8m+15}{40356300937500\times 6^{25+13}\times 6^{311}}$$

Add $25$ and $13$ to get $38$.

$$\frac{8m+15}{40356300937500\times 6^{38}\times 6^{311}}$$

Calculate $6$ to the power of $38$ and get $371319292745659279662190166016$.

$$\frac{8m+15}{40356300937500\times 371319292745659279662190166016\times 6^{311}}$$

Multiply $40356300937500$ and $371319292745659279662190166016$ to get $14985073121943486536886819680094781440000000$.

$$\frac{8m+15}{14985073121943486536886819680094781440000000\times 6^{311}}$$

Calculate $6$ to the power of $311$ and get $101166999457260290972946408167582245513056781009004242408475802665462964110731265705429778469051933906990317572469078367248760400767199701172900643785605734880759997477508781123122516522118319601807898070459516585158471196287836478941016621056$.

$$\frac{8m+15}{14985073121943486536886819680094781440000000\times 101166999457260290972946408167582245513056781009004242408475802665462964110731265705429778469051933906990317572469078367248760400767199701172900643785605734880759997477508781123122516522118319601807898070459516585158471196287836478941016621056}$$

Multiply $14985073121943486536886819680094781440000000$ and $101166999457260290972946408167582245513056781009004242408475802665462964110731265705429778469051933906990317572469078367248760400767199701172900643785605734880759997477508781123122516522118319601807898070459516585158471196287836478941016621056$ to get $1515994884394662476524499437280785345956577875140587751924236707484802630490488991890984457063204806845689953409446372909646786841138594074413474381400857492432519525755109339525046093680972490991907337714835349710654021250668393533360000230277403818224032996734122412487622000640000000$.

$$\frac{8m+15}{1515994884394662476524499437280785345956577875140587751924236707484802630490488991890984457063204806845689953409446372909646786841138594074413474381400857492432519525755109339525046093680972490991907337714835349710654021250668393533360000230277403818224032996734122412487622000640000000}$$

Differentiate w.r.t. m

$\frac{1}{189499360549332809565562429660098168244572234392573468990529588435600328811311123986373057132900600855711244176180796613705848355142324259301684297675107186554064940719388667440630761710121561373988417214354418713831752656333549191670000028784675477278004124591765301560952750080000000} = 5.277062661853509 \times 10^{-285}$