Solve ((7)/(4))^(4)-((7)/(3))^(4)/((7)/(4))^(2)-((7)/(3))^(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

$${ \left( \frac{ 7 }{ 4 } \right) }^{ 4 } - { \left( \frac{ 7 }{ 3 } \right) }^{ 4 } / { \left( \frac{ 7 }{ 4 } \right) }^{ 2 } - { \left( \frac{ 7 }{ 3 } \right) }^{ 2 }$$

Evaluate

$-\frac{119119}{20736}\approx -5.74455054$

Solution Steps

Calculate $\frac{7}{4}$ to the power of $4$ and get $\frac{2401}{256}$.

$$\frac{2401}{256}-\frac{\left(\frac{7}{3}\right)^{4}}{\left(\frac{7}{4}\right)^{2}}-\left(\frac{7}{3}\right)^{2}$$

Calculate $\frac{7}{3}$ to the power of $4$ and get $\frac{2401}{81}$.

$$\frac{2401}{256}-\frac{\frac{2401}{81}}{\left(\frac{7}{4}\right)^{2}}-\left(\frac{7}{3}\right)^{2}$$

Calculate $\frac{7}{4}$ to the power of $2$ and get $\frac{49}{16}$.

$$\frac{2401}{256}-\frac{\frac{2401}{81}}{\frac{49}{16}}-\left(\frac{7}{3}\right)^{2}$$

Divide $\frac{2401}{81}$ by $\frac{49}{16}$ by multiplying $\frac{2401}{81}$ by the reciprocal of $\frac{49}{16}$.

$$\frac{2401}{256}-\frac{2401}{81}\times \frac{16}{49}-\left(\frac{7}{3}\right)^{2}$$

Multiply $\frac{2401}{81}$ times $\frac{16}{49}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{2401}{256}-\frac{2401\times 16}{81\times 49}-\left(\frac{7}{3}\right)^{2}$$

Do the multiplications in the fraction $\frac{2401\times 16}{81\times 49}$.

$$\frac{2401}{256}-\frac{38416}{3969}-\left(\frac{7}{3}\right)^{2}$$

Reduce the fraction $\frac{38416}{3969}$ to lowest terms by extracting and canceling out $49$.

$$\frac{2401}{256}-\frac{784}{81}-\left(\frac{7}{3}\right)^{2}$$

Least common multiple of $256$ and $81$ is $20736$. Convert $\frac{2401}{256}$ and $\frac{784}{81}$ to fractions with denominator $20736$.

$$\frac{194481}{20736}-\frac{200704}{20736}-\left(\frac{7}{3}\right)^{2}$$

Since $\frac{194481}{20736}$ and $\frac{200704}{20736}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{194481-200704}{20736}-\left(\frac{7}{3}\right)^{2}$$

Subtract $200704$ from $194481$ to get $-6223$.

$$-\frac{6223}{20736}-\left(\frac{7}{3}\right)^{2}$$

Calculate $\frac{7}{3}$ to the power of $2$ and get $\frac{49}{9}$.

$$-\frac{6223}{20736}-\frac{49}{9}$$

Least common multiple of $20736$ and $9$ is $20736$. Convert $-\frac{6223}{20736}$ and $\frac{49}{9}$ to fractions with denominator $20736$.

$$-\frac{6223}{20736}-\frac{112896}{20736}$$

Since $-\frac{6223}{20736}$ and $\frac{112896}{20736}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-6223-112896}{20736}$$

Subtract $112896$ from $-6223$ to get $-119119$.

$$-\frac{119119}{20736}$$

Factor

$-\frac{119119}{20736} = -5\frac{15439}{20736} = -5.7445505401234565$