Find the value of m which satisfies
$(\frac{11}{10})^{7} \times (\frac{10}{11})^{10} \times (\frac{11}{10})^{9} = (\frac{10}{11})^{3m+17}$

$-29/3$

$-23/3$

$-15/3$

$-19/3$

APEDIA

NTPC Graduate Tier 1

2025 • 06 Jun, 2025 • Shift-3

Find the value of m which satisfies
$(\frac{11}{10})^{7} \times (\frac{10}{11})^{10} \times (\frac{11}{10})^{9} = (\frac{10}{11})^{3m+17}$

Correct Answer

$-23/3$

Unifying Bases: The equation features two bases: $(11/10)$ and $(10/11)$. We know that $(11/10) = (10/11)^{-1}$. It's optimal to convert all bases to $(10/11)$ ......

💡 Analysis & Explanation

Unifying Bases ▼

The equation features two bases: $(11/10)$ and $(10/11)$. We know that $(11/10) = (10/11)^{-1}$. It's optimal to convert all bases to $(10/11)$ to match the right side.

Converting Terms ▼

Let's convert the $(11/10)$ terms: $(11/10)^7 = (10/11)^{-7}$ and $(11/10)^9 = (10/11)^{-9}$.

Applying Exponent Rules ▼

Substitute these back into the equation: $(10/11)^{-7} \times (10/11)^{10} \times (10/11)^{-9} = (10/11)^{3m+17}$. Using the rule $a^m \times a^n = a^{m+n}$, the left side becomes $(10/11)^{-7 + 10 - 9} = (10/11)^{-6}$.

Solving for m ▼

Equating the exponents since the bases are identical: $-6 = 3m + 17$. This gives $3m = -6 - 17 = -23$, leading to $m = -23/3$.

Conclusion ▼

The value of m is -23/3.

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Find the value of m which satisfies$(\frac{11}{10})^{7} \times (\frac{10}{11})^{10} \times (\frac{11}{10})^{9} = (\frac{10}{11})^{3m+17}$

Find the value of m which satisfies
$(\frac{11}{10})^{7} \times (\frac{10}{11})^{10} \times (\frac{11}{10})^{9} = (\frac{10}{11})^{3m+17}$