Solve 4*(-5/4)^3+3*(-5/4)^2-45/4*(-5/4)+frac{17}{16}=

$$4 \cdot ( - \frac { 5 } { 4 } ) ^ { 3 } + 3 \cdot ( - \frac { 5 } { 4 } ) ^ { 2 } - \frac { 45 } { 4 } \cdot ( - \frac { 5 } { 4 } ) + \frac { 17 } { 16 } =$$

Evaluate

$$12$$

Solution Steps

Calculate -\frac{5}{4} to the power of 3 and get -\frac{125}{64}.

$$4\left(-\frac{125}{64}\right)+3\left(-\frac{5}{4}\right)^{2}-\frac{45}{4}\left(-\frac{5}{4}\right)+\frac{17}{16}$$

Express 4\left(-\frac{125}{64}\right) as a single fraction.

$$\frac{4\left(-125\right)}{64}+3\left(-\frac{5}{4}\right)^{2}-\frac{45}{4}\left(-\frac{5}{4}\right)+\frac{17}{16}$$

Multiply 4 and -125 to get -500.

$$\frac{-500}{64}+3\left(-\frac{5}{4}\right)^{2}-\frac{45}{4}\left(-\frac{5}{4}\right)+\frac{17}{16}$$

Reduce the fraction \frac{-500}{64} to lowest terms by extracting and canceling out 4.

$$-\frac{125}{16}+3\left(-\frac{5}{4}\right)^{2}-\frac{45}{4}\left(-\frac{5}{4}\right)+\frac{17}{16}$$

Calculate -\frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$-\frac{125}{16}+3\times \frac{25}{16}-\frac{45}{4}\left(-\frac{5}{4}\right)+\frac{17}{16}$$

Express 3\times \frac{25}{16} as a single fraction.

$$-\frac{125}{16}+\frac{3\times 25}{16}-\frac{45}{4}\left(-\frac{5}{4}\right)+\frac{17}{16}$$

Multiply 3 and 25 to get 75.

$$-\frac{125}{16}+\frac{75}{16}-\frac{45}{4}\left(-\frac{5}{4}\right)+\frac{17}{16}$$

Since -\frac{125}{16} and \frac{75}{16} have the same denominator, add them by adding their numerators.

$$\frac{-125+75}{16}-\frac{45}{4}\left(-\frac{5}{4}\right)+\frac{17}{16}$$

Add -125 and 75 to get -50.

$$\frac{-50}{16}-\frac{45}{4}\left(-\frac{5}{4}\right)+\frac{17}{16}$$

Reduce the fraction \frac{-50}{16} to lowest terms by extracting and canceling out 2.

$$-\frac{25}{8}-\frac{45}{4}\left(-\frac{5}{4}\right)+\frac{17}{16}$$

Multiply \frac{45}{4} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{25}{8}-\frac{45\left(-5\right)}{4\times 4}+\frac{17}{16}$$

Do the multiplications in the fraction \frac{45\left(-5\right)}{4\times 4}.

$$-\frac{25}{8}-\frac{-225}{16}+\frac{17}{16}$$

Fraction \frac{-225}{16} can be rewritten as -\frac{225}{16} by extracting the negative sign.

$$-\frac{25}{8}-\left(-\frac{225}{16}\right)+\frac{17}{16}$$

The opposite of -\frac{225}{16} is \frac{225}{16}.

$$-\frac{25}{8}+\frac{225}{16}+\frac{17}{16}$$

Least common multiple of 8 and 16 is 16. Convert -\frac{25}{8} and \frac{225}{16} to fractions with denominator 16.

$$-\frac{50}{16}+\frac{225}{16}+\frac{17}{16}$$

Since -\frac{50}{16} and \frac{225}{16} have the same denominator, add them by adding their numerators.

$$\frac{-50+225}{16}+\frac{17}{16}$$

Add -50 and 225 to get 175.

$$\frac{175}{16}+\frac{17}{16}$$

Since \frac{175}{16} and \frac{17}{16} have the same denominator, add them by adding their numerators.

$$\frac{175+17}{16}$$

Add 175 and 17 to get 192.

$$\frac{192}{16}$$

Divide 192 by 16 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$