Solve {l}{8(-3/8)^3}{-10(-3/8)^2}{-9(-3/8)+3}

$$\left. \begin{array} { l } { 8 ( - \frac { 3 } { 8 } ) ^ { 3 } } \\ { - 10 ( - \frac { 3 } { 8 } ) ^ { 2 } } \\ { - 9 ( - \frac { 3 } { 8 } ) + 3 } \end{array} \right.$$

Evaluate

$$\frac{291}{64}=4.546875$$

Solution Steps

Calculate -\frac{3}{8} to the power of 3 and get -\frac{27}{512}.

$$8\left(-\frac{27}{512}\right)-10\left(-\frac{3}{8}\right)^{2}-9\left(-\frac{3}{8}\right)+3$$

Express 8\left(-\frac{27}{512}\right) as a single fraction.

$$\frac{8\left(-27\right)}{512}-10\left(-\frac{3}{8}\right)^{2}-9\left(-\frac{3}{8}\right)+3$$

Multiply 8 and -27 to get -216.

$$\frac{-216}{512}-10\left(-\frac{3}{8}\right)^{2}-9\left(-\frac{3}{8}\right)+3$$

Reduce the fraction \frac{-216}{512} to lowest terms by extracting and canceling out 8.

$$-\frac{27}{64}-10\left(-\frac{3}{8}\right)^{2}-9\left(-\frac{3}{8}\right)+3$$

Calculate -\frac{3}{8} to the power of 2 and get \frac{9}{64}.

$$-\frac{27}{64}-10\times \frac{9}{64}-9\left(-\frac{3}{8}\right)+3$$

Express 10\times \frac{9}{64} as a single fraction.

$$-\frac{27}{64}-\frac{10\times 9}{64}-9\left(-\frac{3}{8}\right)+3$$

Multiply 10 and 9 to get 90.

$$-\frac{27}{64}-\frac{90}{64}-9\left(-\frac{3}{8}\right)+3$$

Since -\frac{27}{64} and \frac{90}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-27-90}{64}-9\left(-\frac{3}{8}\right)+3$$

Subtract 90 from -27 to get -117.

$$-\frac{117}{64}-9\left(-\frac{3}{8}\right)+3$$

Express 9\left(-\frac{3}{8}\right) as a single fraction.

$$-\frac{117}{64}-\frac{9\left(-3\right)}{8}+3$$

Multiply 9 and -3 to get -27.

$$-\frac{117}{64}-\frac{-27}{8}+3$$

Fraction \frac{-27}{8} can be rewritten as -\frac{27}{8} by extracting the negative sign.

$$-\frac{117}{64}-\left(-\frac{27}{8}\right)+3$$

The opposite of -\frac{27}{8} is \frac{27}{8}.

$$-\frac{117}{64}+\frac{27}{8}+3$$

Least common multiple of 64 and 8 is 64. Convert -\frac{117}{64} and \frac{27}{8} to fractions with denominator 64.

$$-\frac{117}{64}+\frac{216}{64}+3$$

Since -\frac{117}{64} and \frac{216}{64} have the same denominator, add them by adding their numerators.

$$\frac{-117+216}{64}+3$$

Add -117 and 216 to get 99.

$$\frac{99}{64}+3$$

Convert 3 to fraction \frac{192}{64}.

$$\frac{99}{64}+\frac{192}{64}$$

Since \frac{99}{64} and \frac{192}{64} have the same denominator, add them by adding their numerators.

$$\frac{99+192}{64}$$

Add 99 and 192 to get 291.

$$\frac{291}{64}$$

Factor

$$\frac{3 \cdot 97}{2 ^ {6}} = 4\frac{35}{64} = 4.546875$$