Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
The expression (a10×b6×c3)(a9×b3×c6) in simplified form is:
(a1)×(b6)×(c−9)
(a1)×(b1)×(c5)
(a−7)×(b−9)×(c4)
(a−1)×(b−3)×(c3)
(a−1)×(b−3)×(c3)
Subtract the powers of the same variables in the denominator from the numerator: a(9−10), b(3−6), and c(6−3).
Expression to simplify: (a⁹ * b³ * c⁶) / (a¹⁰ * b⁶ * c³)
xnxm=xm−n
Subtract the powers of the same variables in the denominator from the numerator: a(9−10), b(3−6), and c(6−3).
Confusing the order of subtraction, leading to a(10−9) instead of a(9−10), resulting in positive exponents for a and b.
Group variables
Rewrite the expression by grouping terms with the same base: a, b, and c.
(a10a9)×(b6b3)×(c3c6)
Apply quotient rule of exponents
Use the rule xnxm=xm−n for each variable group.
a9−10×b3−6×c6−3
Calculate final powers
Subtract the exponents to find the final simplified expression: 9−10=−1, 3−6=−3, and 6−3=3.
a−1×b−3×c3
D is correct because applying the quotient rule of exponents to each variable gives a(9−10)×b(3−6)×c(6−3)=a−1×b−3×c3.
This concept is fundamental to polynomial division and solving complex algebraic equations in competitive exams like RRB JE.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants