describe how to rewrite an expression with a negative exponent in the numerator
To rewrite an expression with a negative exponent in the numerator, you need to move the term with the negative exponent to the denominator and change the sign of the exponent to positive. For example,
$\frac{1}{x^{-2}}$ can be rewritten as $\frac{x^2}{1}$
To do this, you need to start with the original expression and multiply both the numerator and denominator by $x^2$ since $x^2$ is the reciprocal of $x^{-2}$. This gives us:
$\frac{1}{x^{-2}} \cdot \frac{x^2}{x^2} = \frac{x^2}{1}$
Simplifying, we get:
$\frac{1}{x^{-2}} = x^2$
In other words x^-y = 1/ x^y
Yes, that is correct. A term with a negative exponent can be rewritten by moving the base with the negative exponent to the denominator and changing the sign of the exponent to positive. Therefore, $x^{-y}$ can be rewritten as $\frac{1}{x^y}$.
To rewrite an expression with a negative exponent in the numerator, you can follow these steps:
1. Identify the expression with the negative exponent in the numerator. It will have the form of a variable or a number raised to a negative power, such as x^-2 or 5^-3.
2. Recall that any term with a negative exponent in the numerator can be moved to the denominator by changing the sign of the exponent. This means that x^-2 will become 1/x^2 and 5^-3 will become 1/5^3.
3. Simplify the expression further if possible. For example, if you have 1/x^2, you could write it as x^(-2) = 1/(x^2), which is equivalent.
4. Remember to adjust the other terms in the expression, if any, while maintaining the same value. For instance, if you have an expression like (3x^-2)/(2y^3), then x^-2 can be rewritten as 1/x^2 as mentioned before. The expression would become (3/x^2)/(2y^3), rearranging the terms to incorporate the change.
By following these steps, you can successfully rewrite an expression with a negative exponent in the numerator and convert it to a more simplified form.