Find the value of m which satisfies \(\left(\dfrac{26}{7}\right)^5 \times \left(\dfrac{7}{26}\right)^{11} \times \left(\dfrac{26}{7}\right)^{19} = \left(\dfrac{7}{26}\right)^{9m+17}\)
\(-\tfrac{10}{3}\)
Rewrite everything in terms of \(\left(\tfrac{7}{26}\right)\): \(\left(\tfrac{26}{7}\right)^5 = \left(\tfrac{7}{26}\right)^{-5}\) and \(\left(\tfrac{26}{7}\right)^{19} = \left(\tfrac{7}{26}\right)^{-19}\).
Left side exponent (base \(\tfrac{7}{26}\)): \(-5+11-19 = -13\).
So \(\left(\tfrac{7}{26}\right)^{-13} = \left(\tfrac{7}{26}\right)^{9m+17}\), giving \(9m+17=-13\).
\(9m = -30 \Rightarrow m = -\dfrac{30}{9} = -\dfrac{10}{3}\).
Hence, the value of m is \(-\tfrac{10}{3}\).
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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:
\(\sqrt{46.24}+\sqrt{0.4624}+\sqrt{0.004624}\)
