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The expression (a9×b4×c8)(a4×b3×c4) in simplified form is:
(a7)×(b9)×(c8)
(a−9)×(b−2)×(c−2)
(a7)×(b8)×(c−9)
(a−5)×(b−1)×(c−4)
(a−5)×(b−1)×(c−4)
Subtract the exponent of the denominator from the numerator for each base: a^(4-9), b^(3-4), c^(4-8).
Expression: ((a⁴ * b³ * c⁴) / (a⁹ * b⁴ * c⁸))
xnxm=xm−n
Subtract the exponent of the denominator from the numerator for each base: a^(4-9), b^(3-4), c^(4-8).
Students often subtract numerator from denominator (9-4) instead of (4-9) or forget to apply the rule to each variable individually.
Group bases with same variables
To simplify the expression, we use the exponent rule for division, which states that for any base x, xnxm=xm−n.
a9a4×b4b3×c8c4
Subtract the exponents
Apply the subtraction m−n for each variable exponent: a:4−9=−5, b:3−4=−1, c:4−8=−4.
a4−9×b3−4×c4−8
Final Result
After performing the subtractions, we get the simplified expression as a−5×b−1×c−4.
a−5×b−1×c−4
D is correct because the application of the quotient rule for exponents yields the resulting powers a−5, b−1, and c−4.
These exponent rules are foundational for logarithms and scientific notation problems commonly found in RRB JE and other competitive exams.
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