सरळरूप द्या:

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

Question

Question

Answer 1

अशाप्रकारचे प्रश्न सोडवण्यासाठी खाली दिलेले 'करणी व घातांक' यांच्या नियमांचे पालन करा:

घातांकाचे नियम:

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