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((9)/(8))^((11)/(2))+((3)/(4))^((17)/(2)) Which of the following values is equal to the given value? Choose 1 answer: (A) (3^((39)/(2)))/(2^((67)/(2))) (B) ((15)/(8))^(14) (c) (3^(11)+3^((17)/(2)))/(2^((33)/(2))+2^(17)) (D) (3^(11)*sqrt2+3^(8)*sqrt3)/(2^(17))

(98)112+(34)172 \left(\frac{9}{8}\right)^{\frac{11}{2}}+\left(\frac{3}{4}\right)^{\frac{17}{2}} \newlineWhich of the following values is equal to the given value?\newlineChoose 11 answer:\newline(A) 33922672 \frac{3^{\frac{39}{2}}}{2^{\frac{67}{2}}} \newline(B) (158)14 \left(\frac{15}{8}\right)^{14} \newline(C) 311+31722332+217 \frac{3^{11}+3^{\frac{17}{2}}}{2^{\frac{33}{2}}+2^{17}} \newline(D) 311⋅2+38⋅3217 \frac{3^{11} \cdot \sqrt{2}+3^{8} \cdot \sqrt{3}}{2^{17}}

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Full solution

Q. (98)112+(34)172 \left(\frac{9}{8}\right)^{\frac{11}{2}}+\left(\frac{3}{4}\right)^{\frac{17}{2}} \newlineWhich of the following values is equal to the given value?\newlineChoose 11 answer:\newline(A) 33922672 \frac{3^{\frac{39}{2}}}{2^{\frac{67}{2}}} \newline(B) (158)14 \left(\frac{15}{8}\right)^{14} \newline(C) 311+31722332+217 \frac{3^{11}+3^{\frac{17}{2}}}{2^{\frac{33}{2}}+2^{17}} \newline(D) 311⋅2+38⋅3217 \frac{3^{11} \cdot \sqrt{2}+3^{8} \cdot \sqrt{3}}{2^{17}}
  1. Rephrasing the problem: First, let's rephrase the ＂Which option is equivalent to the expression (98)112+(34)172\left(\frac{9}{8}\right)^{\frac{11}{2}}+\left(\frac{3}{4}\right)^{\frac{17}{2}}?＂
  2. Analyzing the expression and answer choices: Now, let's analyze the given expression and the answer choices. We have the expression (98)112+(34)172\left(\frac{9}{8}\right)^{\frac{11}{2}}+\left(\frac{3}{4}\right)^{\frac{17}{2}}. We can simplify this by recognizing that 9=329 = 3^2 and 3=313 = 3^1, and similarly for the denominators where 8=238 = 2^3 and 4=224 = 2^2.
  3. Simplifying the expression: Rewrite the expression using the base numbers 33 and 22: (3223)112+(3122)172\left(\frac{3^2}{2^3}\right)^{\frac{11}{2}} + \left(\frac{3^1}{2^2}\right)^{\frac{17}{2}}. Now we can apply the exponent to both the numerator and the denominator separately.
  4. Applying the exponent to the first term: Applying the exponent to the first term: ((32)(112))/((23)(112))=(32∗(112))/(23∗(112))=311/2332\left(\left(3^2\right)^{\left(\frac{11}{2}\right)}\right)/\left(\left(2^3\right)^{\left(\frac{11}{2}\right)}\right) = \left(3^{2*\left(\frac{11}{2}\right)}\right)/\left(2^{3*\left(\frac{11}{2}\right)}\right) = 3^{11}/2^{\frac{33}{2}}.
  5. Applying the exponent to the second term: Applying the exponent to the second term: (31)(172)/(22)(172)=31∗(172)/22∗(172)=3172/217\left(3^1\right)^{\left(\frac{17}{2}\right)}/\left(2^2\right)^{\left(\frac{17}{2}\right)} = 3^{1*\left(\frac{17}{2}\right)}/2^{2*\left(\frac{17}{2}\right)} = 3^{\frac{17}{2}}/2^{17}.
  6. Combining the two terms: Combine the two terms: (311/233/2)+(317/2/217)(3^{11}/2^{33/2}) + (3^{17/2}/2^{17}). To add these fractions, we need a common denominator, which would be 2172^{17}.
  7. Getting a common denominator: To get a common denominator for the first term, multiply both the numerator and the denominator by 2(17−332)=212=22^{(17 - \frac{33}{2})} = 2^{\frac{1}{2}} = \sqrt{2}: (311⋅2)/217(3^{11} \cdot \sqrt{2}) / 2^{17}.
  8. Comparing with answer choices: Now we have a common denominator for both terms: (311⋅2+3172)/217(3^{11} \cdot \sqrt{2} + 3^{\frac{17}{2}}) / 2^{17}.
  9. Correcting the discrepancy: Let's compare this result with the answer choices. We can see that choice (D) matches our result: (3112+383)/(217)(3^{11}\sqrt{2}+3^{8}\sqrt{3})/(2^{17}). However, there is a slight discrepancy with the second term in the numerator. We have 317/23^{17/2}, which is not the same as 38⋅33^8 \cdot \sqrt{3}. We need to correct this.

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