Solve aleft(-1/2505^4+3/2505^2right)+5

$$a \left( - \frac{ 1 }{ 250 } { 5 }^{ 4 } + \frac{ 3 }{ 250 } { 5 }^{ 2 } \right) +5$$

Evaluate

$$-\frac{11a}{5}+5$$

Solution Steps

Calculate 5 to the power of 4 and get 625.

$$a\left(-\frac{1}{250}\times 625+\frac{3}{250}\times 5^{2}\right)+5$$

Express -\frac{1}{250}\times 625 as a single fraction.

$$a\left(\frac{-625}{250}+\frac{3}{250}\times 5^{2}\right)+5$$

Reduce the fraction \frac{-625}{250} to lowest terms by extracting and canceling out 125.

$$a\left(-\frac{5}{2}+\frac{3}{250}\times 5^{2}\right)+5$$

Calculate 5 to the power of 2 and get 25.

$$a\left(-\frac{5}{2}+\frac{3}{250}\times 25\right)+5$$

Express \frac{3}{250}\times 25 as a single fraction.

$$a\left(-\frac{5}{2}+\frac{3\times 25}{250}\right)+5$$

Multiply 3 and 25 to get 75.

$$a\left(-\frac{5}{2}+\frac{75}{250}\right)+5$$

Reduce the fraction \frac{75}{250} to lowest terms by extracting and canceling out 25.

$$a\left(-\frac{5}{2}+\frac{3}{10}\right)+5$$

Least common multiple of 2 and 10 is 10. Convert -\frac{5}{2} and \frac{3}{10} to fractions with denominator 10.

$$a\left(-\frac{25}{10}+\frac{3}{10}\right)+5$$

Since -\frac{25}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$a\times \frac{-25+3}{10}+5$$

Add -25 and 3 to get -22.

$$a\times \frac{-22}{10}+5$$

Reduce the fraction \frac{-22}{10} to lowest terms by extracting and canceling out 2.

$$a\left(-\frac{11}{5}\right)+5$$

Expand

$$-\frac{11a}{5}+5$$

Solution Steps

Calculate 5 to the power of 4 and get 625.

$$a\left(-\frac{1}{250}\times 625+\frac{3}{250}\times 5^{2}\right)+5$$

Express -\frac{1}{250}\times 625 as a single fraction.

$$a\left(\frac{-625}{250}+\frac{3}{250}\times 5^{2}\right)+5$$

Reduce the fraction \frac{-625}{250} to lowest terms by extracting and canceling out 125.

$$a\left(-\frac{5}{2}+\frac{3}{250}\times 5^{2}\right)+5$$

Calculate 5 to the power of 2 and get 25.

$$a\left(-\frac{5}{2}+\frac{3}{250}\times 25\right)+5$$

Express \frac{3}{250}\times 25 as a single fraction.

$$a\left(-\frac{5}{2}+\frac{3\times 25}{250}\right)+5$$

Multiply 3 and 25 to get 75.

$$a\left(-\frac{5}{2}+\frac{75}{250}\right)+5$$

Reduce the fraction \frac{75}{250} to lowest terms by extracting and canceling out 25.

$$a\left(-\frac{5}{2}+\frac{3}{10}\right)+5$$

Least common multiple of 2 and 10 is 10. Convert -\frac{5}{2} and \frac{3}{10} to fractions with denominator 10.

$$a\left(-\frac{25}{10}+\frac{3}{10}\right)+5$$

Since -\frac{25}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$a\times \frac{-25+3}{10}+5$$

Add -25 and 3 to get -22.

$$a\times \frac{-22}{10}+5$$

Reduce the fraction \frac{-22}{10} to lowest terms by extracting and canceling out 2.

$$a\left(-\frac{11}{5}\right)+5$$