Question
Download Solution PDFലഘൂകരിക്കുക:
\({625^{0.17}} \times {625^{0.08}} = {25^?} \times {25^{ - \frac{3}{2}}}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFഇത്തരത്തിലുള്ള 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
Last updated on Apr 10, 2025
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