Solve 2.7^2+1/2.7^2

$${ 2.7 }^{ 2 } + \frac{ 1 }{ { 2.7 }^{ 2 } }$$

Evaluate

$$\frac{541441}{72900}\approx 7.427174211$$

Solution Steps

Calculate 2.7 to the power of 2 and get 7.29.

$$7.29+\frac{1}{2.7^{2}}$$

Calculate 2.7 to the power of 2 and get 7.29.

$$7.29+\frac{1}{7.29}$$

Expand \frac{1}{7.29} by multiplying both numerator and the denominator by 100.

$$7.29+\frac{100}{729}$$

Convert decimal number 7.29 to fraction \frac{729}{100}.

$$\frac{729}{100}+\frac{100}{729}$$

Least common multiple of 100 and 729 is 72900. Convert \frac{729}{100} and \frac{100}{729} to fractions with denominator 72900.

$$\frac{531441}{72900}+\frac{10000}{72900}$$

Since \frac{531441}{72900} and \frac{10000}{72900} have the same denominator, add them by adding their numerators.

$$\frac{531441+10000}{72900}$$

Add 531441 and 10000 to get 541441.

$$\frac{541441}{72900}$$

Factor

$$\frac{73 \cdot 7417}{2 ^ {2} \cdot 3 ^ {6} \cdot 5 ^ {2}} = 7\frac{31141}{72900} = 7.4271742112482855$$