Answer
28. \( 1 \)
29. \( \frac{8}{27} \)
30. \( 0 \)
31. \( \frac{5}{12} \)
32. \( \frac{8}{13} \)
Solution
Calculate the value by following steps:
- step0: Calculate:
\(\left(\frac{2}{3}\right)^{3}\)
- step1: Use the properties of exponents:
\(\frac{2^{3}}{3^{3}}\)
- step2: Evaluate the power:
\(\frac{8}{3^{3}}\)
- step3: Evaluate the power:
\(\frac{8}{27}\)
Calculate or simplify the expression \( 25/19 - 6/19 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{25}{19}-\frac{6}{19}\)
- step1: Transform the expression:
\(\frac{25-6}{19}\)
- step2: Subtract the numbers:
\(\frac{19}{19}\)
- step3: Reduce the numbers:
\(\frac{1}{1}\)
- step4: Calculate:
\(1\)
Calculate or simplify the expression \( (4/3) * (3/7) / (13/14) \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\frac{4}{3}\times \frac{3}{7}}{\frac{13}{14}}\)
- step1: Multiply the numbers:
\(\frac{\frac{4}{7}}{\frac{13}{14}}\)
- step2: Multiply by the reciprocal:
\(\frac{4}{7}\times \frac{14}{13}\)
- step3: Reduce the numbers:
\(4\times \frac{2}{13}\)
- step4: Multiply:
\(\frac{4\times 2}{13}\)
- step5: Multiply:
\(\frac{8}{13}\)
Calculate or simplify the expression \( \sqrt(48/2) - \sqrt(7*3 + 39/13) \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{\frac{48}{2}}-\sqrt{7\times 3+\frac{39}{13}}\)
- step1: Divide the terms:
\(\sqrt{\frac{48}{2}}-\sqrt{7\times 3+3}\)
- step2: Multiply the numbers:
\(\sqrt{\frac{48}{2}}-\sqrt{21+3}\)
- step3: Divide the terms:
\(\sqrt{24}-\sqrt{21+3}\)
- step4: Add the numbers:
\(\sqrt{24}-\sqrt{24}\)
- step5: Subtract the terms:
\(0\)
Calculate or simplify the expression \( \sqrt(25/144) \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{\frac{25}{144}}\)
- step1: Use the properties of radicals:
\(\frac{\sqrt{25}}{\sqrt{144}}\)
- step2: Simplify the expression:
\(\frac{5}{12}\)
Here are the detailed solutions for each of the problems:
28. **Calculate \( \frac{25}{19} - \frac{6}{19} \)**:
- Since both fractions have the same denominator, we can subtract the numerators directly:
\[
\frac{25 - 6}{19} = \frac{19}{19} = 1
\]
**Result**: \( 1 \)
29. **Calculate \( \left(\frac{2}{3}\right)^{3} \)**:
- To find the cube of a fraction, we cube the numerator and the denominator:
\[
\left(\frac{2}{3}\right)^{3} = \frac{2^{3}}{3^{3}} = \frac{8}{27}
\]
**Result**: \( \frac{8}{27} \)
30. **Calculate \( \sqrt{\frac{48}{2}} - \sqrt{7 \cdot 3 + \frac{39}{13}} \)**:
- First, simplify \( \frac{48}{2} \):
\[
\sqrt{\frac{48}{2}} = \sqrt{24}
\]
- Next, simplify \( 7 \cdot 3 + \frac{39}{13} \):
\[
7 \cdot 3 = 21 \quad \text{and} \quad \frac{39}{13} = 3 \quad \Rightarrow \quad 21 + 3 = 24
\]
- Now, we have:
\[
\sqrt{24} - \sqrt{24} = 0
\]
**Result**: \( 0 \)
31. **Calculate \( \sqrt{\frac{25}{144}} \)**:
- To find the square root of a fraction, we take the square root of the numerator and the denominator:
\[
\sqrt{\frac{25}{144}} = \frac{\sqrt{25}}{\sqrt{144}} = \frac{5}{12}
\]
**Result**: \( \frac{5}{12} \)
32. **Calculate \( \frac{4}{3} \cdot \frac{3}{7} \div \frac{13}{14} \)**:
- First, convert the division into multiplication by the reciprocal:
\[
\frac{4}{3} \cdot \frac{3}{7} \cdot \frac{14}{13}
\]
- Now, multiply the fractions:
\[
= \frac{4 \cdot 3 \cdot 14}{3 \cdot 7 \cdot 13}
\]
- The \( 3 \) in the numerator and denominator cancels out:
\[
= \frac{4 \cdot 14}{7 \cdot 13} = \frac{56}{91}
\]
- Simplifying \( \frac{56}{91} \) gives:
\[
= \frac{8}{13}
\]
**Result**: \( \frac{8}{13} \)
In summary, the results are:
- 28: \( 1 \)
- 29: \( \frac{8}{27} \)
- 30: \( 0 \)
- 31: \( \frac{5}{12} \)
- 32: \( \frac{8}{13} \)
Answered by UpStudy AI and reviewed by a Professional Tutor
Explain
Simplify this solution
