Find the value of m which satisfies \(\left(\dfrac{22}{5}\right)^{18} \times \left(\dfrac{5}{22}\right)^{8} \times \left(\dfrac{22}{5}\right)^{6} = \left(\dfrac{5}{22}\right)^{9m+4}.\)
\(-\dfrac{20}{9}\)
Left side: \(\left(\dfrac{22}{5}\right)^{18}\times\left(\dfrac{5}{22}\right)^{8}\times\left(\dfrac{22}{5}\right)^{6} = \left(\dfrac{22}{5}\right)^{18+6}\times\left(\dfrac{22}{5}\right)^{-8} = \left(\dfrac{22}{5}\right)^{16}\).
Right side: \(\left(\dfrac{5}{22}\right)^{9m+4} = \left(\dfrac{22}{5}\right)^{-(9m+4)}\).
Equating exponents: \(16 = -(9m+4) \Rightarrow 9m+4 = -16 \Rightarrow 9m = -20 \Rightarrow m = -\dfrac{20}{9}\).
Hence, the value of m is \(-\tfrac{20}{9}\).
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Important Questions from Surds and Indices
The value of \(\frac{{{{\left( {251} \right)}^3} + {{\left( {249} \right)}^3}}}{{25.1 \times 25.1 - 624.99 + 24.9 \times 24.9}}\) is 5 × 10 k , where the value of k is :
Find the value of m in \(\left(\frac{2}{7}\right)^{-3} \times \left(\frac{2}{7}\right)^{-5}=\left (\frac{2}{7}\right)^{-3m+1}\)
If √625 = 25; then√(.00000625/25)is:
A. 0.0025
B. 0.001
C. 0.0001
D. 0.0005Find the value of:
\(\sqrt{150}-\sqrt{54}-\sqrt{24}\)
If \(\sqrt{4624}=68\) , then the value of:
\(\sqrt{46.24}+\sqrt{0.4624}+\sqrt{0.004624}\)
