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Evaluate the given expression. 23×(−9)0×33
81
216
36
9
216
Recall that any non-zero number raised to the power of 0 equals 1. Thus, (-9)0 = 1, simplifying the expression to 2³ ×3³ = (2 \times$$3)^3 = 6³ = 216.
Expression: 2³ \times (-$$9)^0 \times 3³
a0=1,am×bm=(a×b)m
Recall that any non-zero number raised to the power of 0 equals 1. Thus, (-9)0 = 1, simplifying the expression to 2³ ×3³ = (2 \times$$3)^3 = 6³ = 216.
Students often mistakenly assume that (-9)0 equals 0 or -1, whereas any non-zero base raised to the zero exponent is always 1.
Step 1: Simplify the zero exponent term
Any non-zero real number raised to the power of zero is 1. Therefore, (−9)0=1.
(−9)0=1
Step 2: Evaluate individual powers
Calculate 23 and 33 separately: 23=2×2×2=8 and 33=3×3×3=27.
23=8,33=27
Step 3: Multiply the evaluated terms
Substitute the values back into the expression: 8×1×27=8×27.
8×27=216
B is correct because evaluating 23×(−9)0×33 gives 8×1×27=216.
Understanding exponent laws is crucial for simplifying complex algebraic expressions and solving polynomial equations quickly in quantitative aptitude exams.
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