Solve ((4)^(2))/((7)^(2))((4)^(2))/((8)^(2))((4)^(2))/((9)^(2))+4 | 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

$$\frac{ { 4 }^{ 2 } }{ { 7 }^{ 2 } } \frac{ { 4 }^{ 2 } }{ { 8 }^{ 2 } } \frac{ { 4 }^{ 2 } }{ { 9 }^{ 2 } } +4$$

Evaluate

$\frac{15940}{3969}\approx 4.016124969$

Solution Steps

Calculate $4$ to the power of $2$ and get $16$.

$$\frac{16}{7^{2}}\times \frac{4^{2}}{8^{2}}\times \frac{4^{2}}{9^{2}}+4$$

Calculate $7$ to the power of $2$ and get $49$.

$$\frac{16}{49}\times \frac{4^{2}}{8^{2}}\times \frac{4^{2}}{9^{2}}+4$$

Calculate $4$ to the power of $2$ and get $16$.

$$\frac{16}{49}\times \frac{16}{8^{2}}\times \frac{4^{2}}{9^{2}}+4$$

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

$$\frac{16}{49}\times \frac{16}{64}\times \frac{4^{2}}{9^{2}}+4$$

Reduce the fraction $\frac{16}{64}$ to lowest terms by extracting and canceling out $16$.

$$\frac{16}{49}\times \frac{1}{4}\times \frac{4^{2}}{9^{2}}+4$$

Multiply $\frac{16}{49}$ times $\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 1}{49\times 4}\times \frac{4^{2}}{9^{2}}+4$$

Do the multiplications in the fraction $\frac{16\times 1}{49\times 4}$.

$$\frac{16}{196}\times \frac{4^{2}}{9^{2}}+4$$

Reduce the fraction $\frac{16}{196}$ to lowest terms by extracting and canceling out $4$.

$$\frac{4}{49}\times \frac{4^{2}}{9^{2}}+4$$

Calculate $4$ to the power of $2$ and get $16$.

$$\frac{4}{49}\times \frac{16}{9^{2}}+4$$

Calculate $9$ to the power of $2$ and get $81$.

$$\frac{4}{49}\times \frac{16}{81}+4$$

Multiply $\frac{4}{49}$ times $\frac{16}{81}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 16}{49\times 81}+4$$

Do the multiplications in the fraction $\frac{4\times 16}{49\times 81}$.

$$\frac{64}{3969}+4$$

Convert $4$ to fraction $\frac{15876}{3969}$.

$$\frac{64}{3969}+\frac{15876}{3969}$$

Since $\frac{64}{3969}$ and $\frac{15876}{3969}$ have the same denominator, add them by adding their numerators.

$$\frac{64+15876}{3969}$$

Add $64$ and $15876$ to get $15940$.

$$\frac{15940}{3969}$$

Factor

$\frac{2 ^ {2} \cdot 5 \cdot 797}{3 ^ {4} \cdot 7 ^ {2}} = 4\frac{64}{3969} = 4.016124968505921$