Solve =-7(3/4)^2+8(3/4)^3-3(3/4)^4+6

$$= - 7 ( \frac { 3 } { 4 } ) ^ { 2 } + 8 ( \frac { 3 } { 4 } ) ^ { 3 } - 3 ( \frac { 3 } { 4 } ) ^ { 4 } + 6$$

Evaluate

$$\frac{1149}{256}=4.48828125$$

Solution Steps

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$-7\times \frac{9}{16}+8\times \left(\frac{3}{4}\right)^{3}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Express -7\times \frac{9}{16} as a single fraction.

$$\frac{-7\times 9}{16}+8\times \left(\frac{3}{4}\right)^{3}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Multiply -7 and 9 to get -63.

$$\frac{-63}{16}+8\times \left(\frac{3}{4}\right)^{3}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Fraction \frac{-63}{16} can be rewritten as -\frac{63}{16} by extracting the negative sign.

$$-\frac{63}{16}+8\times \left(\frac{3}{4}\right)^{3}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Calculate \frac{3}{4} to the power of 3 and get \frac{27}{64}.

$$-\frac{63}{16}+8\times \frac{27}{64}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Express 8\times \frac{27}{64} as a single fraction.

$$-\frac{63}{16}+\frac{8\times 27}{64}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Multiply 8 and 27 to get 216.

$$-\frac{63}{16}+\frac{216}{64}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Reduce the fraction \frac{216}{64} to lowest terms by extracting and canceling out 8.

$$-\frac{63}{16}+\frac{27}{8}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Least common multiple of 16 and 8 is 16. Convert -\frac{63}{16} and \frac{27}{8} to fractions with denominator 16.

$$-\frac{63}{16}+\frac{54}{16}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Since -\frac{63}{16} and \frac{54}{16} have the same denominator, add them by adding their numerators.

$$\frac{-63+54}{16}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Add -63 and 54 to get -9.

$$-\frac{9}{16}-3\times \left(\frac{3}{4}\right)^{4}+6$$

Calculate \frac{3}{4} to the power of 4 and get \frac{81}{256}.

$$-\frac{9}{16}-3\times \frac{81}{256}+6$$

Express 3\times \frac{81}{256} as a single fraction.

$$-\frac{9}{16}-\frac{3\times 81}{256}+6$$

Multiply 3 and 81 to get 243.

$$-\frac{9}{16}-\frac{243}{256}+6$$

Least common multiple of 16 and 256 is 256. Convert -\frac{9}{16} and \frac{243}{256} to fractions with denominator 256.

$$-\frac{144}{256}-\frac{243}{256}+6$$

Since -\frac{144}{256} and \frac{243}{256} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-144-243}{256}+6$$

Subtract 243 from -144 to get -387.

$$-\frac{387}{256}+6$$

Convert 6 to fraction \frac{1536}{256}.

$$-\frac{387}{256}+\frac{1536}{256}$$

Since -\frac{387}{256} and \frac{1536}{256} have the same denominator, add them by adding their numerators.

$$\frac{-387+1536}{256}$$

Add -387 and 1536 to get 1149.

$$\frac{1149}{256}$$

Factor

$$\frac{3 \cdot 383}{2 ^ {8}} = 4\frac{125}{256} = 4.48828125$$