ലഘൂകരിക്കുക:

\({625^{0.17}} \times {625^{0.08}} = {25^?} \times {25^{ - \frac{3}{2}}}\)

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  1. 1
  2. 2
  3. 3
  4. 0.5

Answer (Detailed Solution Below)

Option 2 : 2
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ഇത്തരത്തിലുള്ള ചോദ്യങ്ങൾ‌ പരിഹരിക്കുന്നതിന്, ചുവടെ നൽകിയിരിക്കുന്ന “കരണികളുടെയും  കൃത്യങ്കങ്ങളുടെയും” നിയമങ്ങൾ‌ പാലിക്കുക:

കൃത്യങ്ക നിയമങ്ങൾ:

1. am × an = a{m + n}

2. am ÷ an = a{m - n}

3. (am)n = amn

4. (a)-m = 1/am

5. (a)m/n = n√am

6. (a)0 = 1

\({625^{0.17}} \times {625^{0.08}} = {25^?} \times {25^{- \frac{3}{2}}}\)

\(\Rightarrow {625^{0.17\; + \;0.08}} = {25^{? + (- \frac{3}{2})}}\)

\(\Rightarrow {625^{0.25}} = {25^{? - \frac{3}{2}}}\)

\(\Rightarrow {625^{\frac{1}{4}}} = {\left( {{5^2}} \right)^{? - \frac{3}{2}}}\)

\(\Rightarrow 5 = {5^{2 \times? - 3}}\)

⇒ 2 × ? - 3 = 1

⇒ ? = (1 + 3)/2

∴ ? = 2

Latest Kerala PSC Civil Excise Officer Updates

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-> The Kerala PSC Civil Excise Officer Notification 2025 has bee released (Advt No. 743/2024). 

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