One noticeable difference between negative and positive exponents is their effect on the value of a number or expression.
Positive exponents represent repeated multiplication. For example, if we have a number, say 2, raised to the power of 3 (2³), it means multiplying 2 by itself three times. So, 2³ = 2 × 2 × 2 = 8. In general, positive exponents make numbers or expressions larger.
On the other hand, negative exponents represent the reciprocal or inverse of the base number raised to that power. For example, if we have a number, say 2, raised to the power of -3 (2⁻³), it means taking the reciprocal of 2 cubed. So, 2⁻³ = 1/(2³) = 1/8. In general, negative exponents make numbers or expressions smaller.
Additionally, negative exponents can also be interpreted as powers of the reciprocal of the base number. For instance, 2⁻³ = (1/2)³ = 1/8.
Another difference is that positive exponents always result in a positive number (except for 0 raised to a positive exponent, which gives 0), while negative exponents typically result in fractions or decimals.
Furthermore, in algebra, negative exponents can be rewritten using positive exponents by moving the base number to the opposite side of the fraction line. For example, x⁻³ can be written as 1/x³.
Overall, negative exponents have the opposite effect of positive exponents on the value of a number or expression and can often be converted to positive exponents.
What do you notice between negatives and positive exponents
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