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 \(-\tfrac{20}{9}\).
Similar Questions
- Given that $7^{0.07} = x$, $7^{0.07} = y$ and $x^z = y^3$, then the value of z is close to:
- Given that $76^{0.44} = x$, $76^{0.93} = y$ and $x^z = y^3$, then the value of z is close to:
- Find the value of $57^{-8} \div 57^{17} \times 57^{-18}$.
- Find the value of: $93^{-6} \div 93^{16} \times 93^{-12}$
- The square root of $\frac{(3\frac{1}{4})^{4} - (4\frac{1}{3})^{4}}{(3\frac{1}{4})^{2} - (4\frac{1}{3})^{2}}$ is:
- Simplify: $(1^3 + 2^3 + 3^3 + \dots + 8^3)^{\frac{-5}{2}}$
- If $\sqrt{54} + \sqrt{150} = 19.60$, then what will the value of $\sqrt{216} + \sqrt{96}$ be? Give your answer, correct to one decimal place.
- Solve the following:
$(625)^{0.17} \times (625)^{0.08} = ?$ - If $\frac{9^m \times 3^5 \times 27^3}{3 \times 81^4} = 3^9$, then the value of m is:
- If $\sqrt{45} + \sqrt{125} = 17.88$ then what will be the value of $\sqrt{180} + \sqrt{80}$ ?
Important Questions from Surds and Indices
The value of (0.3) [{(200 - 146)/(3 × 3 × 3)} - 3] is:
The expression \(\frac{{15\left( {\sqrt {10} + \sqrt 5 } \right)}}{{\sqrt {10\;} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}\) is equal to:
Let \(x = \left( {\frac{{√ {1875} }}{{√ {3888} }} \div \frac{{√ {1200} }}{{\sqrt 768}}} \right) \times \frac{{√ {175} }}{{√ {1792} }}\) . Then √x is equal to:
If \(x = \sqrt {-\sqrt 3 + \sqrt {3 + 8\sqrt {7 + 4\sqrt 3}}}\) where x > 0, then the value of x is equal to:
What is the value of \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}−\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}−\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}\) ?
