Find the value of \(m\) which satisfies \(\left(\frac{28}{8}\right)^{17} \times \left(\frac{8}{28}\right)^{20} \times \left(\frac{28}{8}\right)^{3} = \left(\frac{8}{28}\right)^{9m + 14}\).
\(-\frac{14}{9}\)
Combine the two powers of \(\frac{28}{8}\) on the left by adding exponents: \(\left(\frac{28}{8}\right)^{17} \times \left(\frac{28}{8}\right)^{3} = \left(\frac{28}{8}\right)^{20}\).
The left side is now \(\left(\frac{28}{8}\right)^{20} \times \left(\frac{8}{28}\right)^{20}\), and since \(\frac{28}{8}\) and \(\frac{8}{28}\) are reciprocals, this product equals \(1\).
Write 1 as a power of the base on the right: \(1 = \left(\frac{8}{28}\right)^{0}\).
Equating exponents of the same base gives \(9m + 14 = 0\).
Solve for \(m\): \(9m = -14 \Rightarrow m = -\frac{14}{9}\).
Hence, the value of \(m\) is \(-\frac{14}{9}\).
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:
- Find the value of $57^{-8} \div 57^{17} \times 57^{-18}$.
- If $\sqrt{45} + \sqrt{125} = 17.89$, then what will be the value of $\sqrt{180} + \sqrt{80}$?
(Give your answer to one decimal place.) - What is the value of $\frac{4+\sqrt{2}}{\sqrt{2}+1}$?
If $\sqrt{2916} = 54$ then what is the value of the following?
$\sqrt{29.16} + \sqrt{0.2916} + \sqrt{0.002916} + \sqrt{0.00002916}$
- Find the value of $95^{-17} \div 95^{9} \times 95^{-15}$.
- $(\sqrt{5} + \sqrt{11})(\sqrt{5} - \sqrt{11})$ is equal to:
- What is the value of $\sqrt{75} + \sqrt{147}$?
- Find $\sqrt{\frac{1521}{1849}}$
If $\frac{2\sqrt{2}+\sqrt{7}}{2\sqrt{2}-\sqrt{7}} = x + y\sqrt{14}$, find the value of y.
Important Questions from Surds and Indices
Find the cube root of 78402752
Find the value of :
[(3 × 3 × 3 × 3 × 3 × 3) 6 ÷ (3 × 3 × 3 × 3) 7 × 3 4]
The cube root of - 64 × - 1331 is:
If (27) m = (81) n, then m 2: mn = ?
if 49 n + 49 n + 49 n + 49 n + 49 n + 49 n + 49 n = 7 2221 , then n = ?
