Solve 5600=(1+8.158/12)^48-1/frac{8.158{12}}

$$5600 = \frac { ( 1 + \frac { 8.158 } { 12 } ) ^ { 48 } - 1 } { \frac { 8.158 } { 12 } }$$

Verify

Solution Steps

Expand \frac{8.158}{12} by multiplying both numerator and the denominator by 1000.

$$5600=\frac{\left(1+\frac{8158}{12000}\right)^{48}-1}{\frac{8.158}{12}}$$

Reduce the fraction \frac{8158}{12000} to lowest terms by extracting and canceling out 2.

$$5600=\frac{\left(1+\frac{4079}{6000}\right)^{48}-1}{\frac{8.158}{12}}$$

Add 1 and \frac{4079}{6000} to get \frac{10079}{6000}.

$$5600=\frac{\left(\frac{10079}{6000}\right)^{48}-1}{\frac{8.158}{12}}$$

Calculate \frac{10079}{6000} to the power of 48 and get \frac{1458939792159292439999178741110726478790373224700265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$5600=\frac{\frac{1458939792159292439999178741110726478790373224700265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}-1}{\frac{8.158}{12}}$$

Subtract 1 from \frac{1458939792159292439999178741110726478790373224700265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{1458939792136840182291824183870639267666580549884265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$5600=\frac{\frac{1458939792136840182291824183870639267666580549884265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{8.158}{12}}$$

Expand \frac{8.158}{12} by multiplying both numerator and the denominator by 1000.

$$5600=\frac{\frac{1458939792136840182291824183870639267666580549884265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{8158}{12000}}$$

Reduce the fraction \frac{8158}{12000} to lowest terms by extracting and canceling out 2.

$$5600=\frac{\frac{1458939792136840182291824183870639267666580549884265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{4079}{6000}}$$

Divide \frac{1458939792136840182291824183870639267666580549884265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by \frac{4079}{6000} by multiplying \frac{1458939792136840182291824183870639267666580549884265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by the reciprocal of \frac{4079}{6000}.

$$5600=\frac{1458939792136840182291824183870639267666580549884265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{6000}{4079}$$

Multiply \frac{1458939792136840182291824183870639267666580549884265876614883579439847351000281497770032348154229066079007485193529957266820331997130140332610197976040589282165657066318339632840475118261583361}{22452257707354557240087211123792674816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} and \frac{6000}{4079} to get \frac{357670946834233925543472464788094941815783415024335836385114876057819894827232531936757133648989719558472048343596459246585028682797288632657562632027602177535096118244260758234977964761359}{3742042951225759540014535187298779136000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$5600=\frac{357670946834233925543472464788094941815783415024335836385114876057819894827232531936757133648989719558472048343596459246585028682797288632657562632027602177535096118244260758234977964761359}{3742042951225759540014535187298779136000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Convert 5600 to fraction \frac{20955440526864253424081397048873163161600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3742042951225759540014535187298779136000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{20955440526864253424081397048873163161600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3742042951225759540014535187298779136000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}=\frac{357670946834233925543472464788094941815783415024335836385114876057819894827232531936757133648989719558472048343596459246585028682797288632657562632027602177535096118244260758234977964761359}{3742042951225759540014535187298779136000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Compare \frac{20955440526864253424081397048873163161600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3742042951225759540014535187298779136000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} and \frac{357670946834233925543472464788094941815783415024335836385114876057819894827232531936757133648989719558472048343596459246585028682797288632657562632027602177535096118244260758234977964761359}{3742042951225759540014535187298779136000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\text{false}$$