expressions with possitive and negative exponents. how do u leave no exponents in the denominator?
Change the sign of any exponents in the denominator and put the resulting terms in the numerator.
When working with expressions that involve positive and negative exponents, it is important to understand the rules of exponentiation.
Positive Exponents:
A positive exponent indicates the number of times a base is multiplied by itself. For example, if we have 2 raised to the power of 3, written as 2^3, it means 2 is multiplied by itself 3 times: 2^3 = 2 × 2 × 2 = 8.
Negative Exponents:
A negative exponent indicates that the base is moved to the denominator of a fraction, and it becomes the reciprocal of the positive exponent. For example, if we have 2 raised to the power of -3, written as 2^(-3), it means 2 is taken as the reciprocal and placed in the denominator: 2^(-3) = 1/(2^3) = 1/8.
To get rid of exponents in the denominator, we use the property that a negative exponent can be transformed into a positive exponent by moving the base to the opposite location in the fraction.
Here is an example to illustrate how to eliminate exponents in the denominator:
Expression: (4^2)/(2^(-3))
Step 1: Change the negative exponent to a positive exponent by moving the base to the opposite location in the fraction: (4^2)/(1/(2^3))
Step 2: Simplify the expression in the denominator by flipping the fraction, so it becomes (4^2) * (2^3)
Step 3: Evaluate each exponent: (16) * (8) = 128
Thus, the expression (4^2)/(2^(-3)) simplifies to 128, and there are no more exponents in the denominator.
Remember to always apply the rules of positive and negative exponents to manipulate the expression and simplify it accordingly.