QuestionAugust 27, 2025

(-(8-11)^3-3vert -14vert )/(2^4)-7

(-(8-11)^3-3vert -14vert )/(2^4)-7
(-(8-11)^3-3vert -14vert )/(2^4)-7

Solution
4.7(323 votes)

Answer

\frac{23}{3} or 7.\overline{6} Explanation 1. Simplify the numerator Calculate -(8-11)^{3}: (8-11) = -3, so (-3)^{3} = -27. Thus, -(8-11)^{3} = 27. Calculate 3\vert -14\vert: \vert -14\vert = 14, so 3 \times 14 = 42. Combine: 27 + 42 = 69. 2. Simplify the denominator Calculate 2^{4} - 7: 2^{4} = 16, so 16 - 7 = 9. 3. Divide the simplified numerator by the simplified denominator \frac{69}{9} = 7.666... or \frac{23}{3} in fractional form.

Explanation

1. Simplify the numerator<br /> Calculate $-(8-11)^{3}$: $(8-11) = -3$, so $(-3)^{3} = -27$. Thus, $-(8-11)^{3} = 27$.<br /> Calculate $3\vert -14\vert$: $\vert -14\vert = 14$, so $3 \times 14 = 42$.<br /> Combine: $27 + 42 = 69$.<br /><br />2. Simplify the denominator<br /> Calculate $2^{4} - 7$: $2^{4} = 16$, so $16 - 7 = 9$.<br /><br />3. Divide the simplified numerator by the simplified denominator<br /> $\frac{69}{9} = 7.666...$ or $\frac{23}{3}$ in fractional form.
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