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The value of M, satisfying 23×33×63=6M is:
6
8
4
2
6
Observe that 23×33 is (2×3)3=63. The entire expression becomes 63×63, which is 63+3=66. Thus, M=6.
Expression: 2³ * 3³ * 6³ = 6ᴹ
(an×bn=(a×b)n) and (xa×xb=xa+b)
Observe that 23×33 is (2×3)3=63. The entire expression becomes 63×63, which is 63+3=66. Thus, M=6.
Students often try to calculate the individual values (8×27×216) instead of using exponent laws to simplify the base to 6.
Group bases with the same exponent
Using the law of exponents an×bn=(a×b)n, combine the first two terms: 23×33=(2×3)3=63.
(2×3)3×63=63×63
Apply product rule for exponents
Since the bases are now the same, add the exponents: 63×63=63+3=66.
63+3=66
Equate the powers
Comparing 66=6M, we find the value of M.
M=6
A is correct because the expression simplifies to 6⁶, meaning M = 6.
These exponent rules are frequently tested in simplification and number system problems. Always look to convert mixed bases to a common prime base or the target base.
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