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The value of [(10)150÷(10)146] is:
10000
106
105
1000
10000
Use the laws of exponents: when dividing numbers with the same base, simply subtract the exponents: 150 - 146 = 4. The result is 10⁴ = 10000.
An expression [(10)150 ÷ (10)146]
anam=am−n
Use the laws of exponents: when dividing numbers with the same base, simply subtract the exponents: 150 - 146 = 4. The result is 10⁴ = 10000.
Many students might accidentally add the exponents (150 + 146) instead of subtracting them, or miscalculate the base 10 power as 10⁶ instead of 10⁴.
Identify the base and exponents
The expression is in the form of division of powers with the same base, which is 10. The base is a=10, the dividend exponent is m=150, and the divisor exponent is n=146.
(10)150÷(10)146
Apply quotient rule for exponents
Using the exponent rule anam=am−n, subtract the exponent of the denominator from the exponent of the numerator.
10150−146=104
Calculate the final value
Evaluate 104, which means multiplying 10 by itself 4 times: 10×10×10×10=10000.
104=10000
A is correct because the expression simplifies to 104, which equals 10000.
This is a fundamental rule in algebra; remember that exponents add during multiplication (am×an=am+n) and subtract during division (am÷an=am−n).
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