Apedia Logo Apedia
Join

Choose Language

Select your preferred reading language
🇬🇧
English
✔
🇮🇳
हिन्दी
✔
✕
Full View
Mathematics
Surds and Indices
EN हिंदी
✕
NTPC Graduate Tier 1 2025 Shift-2 📅 05 Jun, 2025

Find the value of m which satisfies (29/4)³ x (4/29)² x (29/4)¹¹ = (4/29)^(9m+7).

A
-19/9
B
-23/9
C
-18/9
D
-10/9
Result Summary
Logo

APEDIA

NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-2
Find the value of m which satisfies (29/4)³ x (4/29)² x (29/4)¹¹ = (4/29)^(9m+7).
Correct Answer
-19/9
Base Harmonization: To effectively solve exponent equations, all terms must share an identical numerical base. We can invert the fraction (4/29) to (29/4) by ne......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Surds and Indices
Pg. No -
💡 Analysis & Explanation
Base Harmonization ▼
To effectively solve exponent equations, all terms must share an identical numerical base. We can invert the fraction (4/29) to (29/4) by negating its exponent.
Exponent Integration ▼
Transform the equation to match bases: (29/4)³ * (29/4)⁻² * (29/4)¹¹ = (29/4)^-(9m+7).
Law of Multiplication ▼
When multiplying identical bases, simply add their powers: 3 + (-2) + 11 = 12. So, the left side consolidates to (29/4)¹².
Algebraic Extraction ▼
Equate the derived powers since the bases are now equal: 12 = -(9m + 7). Distribute the negative: 12 = -9m - 7.
Final Computation ▼
Rearranging yields 9m = -19, isolating 'm' gives -19/9.
Conclusion ▼
The exact fractional value for m is -19/9.
← Prev
64 / 100
Next →