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Find the value of (2⁵ * 2³) / 2⁴.
16
8
32
4
16
Directly sum exponents for multiplication and subtract for division: 5 + 3 - 4 = 4. Then calculate 2⁴ = 16.
Expression involving base 2 with various exponents: 2⁵, 2³, and 2⁴.
amimesan=am+n, anam=am−n
Directly sum exponents for multiplication and subtract for division: 5 + 3 - 4 = 4. Then calculate 2⁴ = 16.
Students often multiply the bases (2*2) or add the bases instead of keeping the base 2 and performing operations on exponents.
Simplify numerator using product rule
Using the product rule amimesan=am+n, add the exponents of the numerator.
25imes23=25+3=28
Simplify expression using quotient rule
Using the quotient rule am/an=am−n, subtract the exponent of the denominator from the numerator's exponent.
rac2824=28−4=24
Calculate final value
Evaluate the power of 2 as 2imes2imes2imes2.
24=16
A is correct because the application of exponent laws 25+3−4 simplifies to 24, which equals 16.
Mastery of exponent laws is essential for solving surds, indices, and logarithmic equations frequently found in RRB competitive exams.