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To solve negative exponents with fractions, we have to use both the negative exponents’ rule and the fractional exponent’s rule. We will look at the process that can be used to simplify expressions that have negative exponents with fractions along with various exercises to improve understanding.
The negative exponent means take the reciprocal, or flip the fraction, so, ( (-27)^-1/3) / 1 = 1 / ( (-27)^1/3), and the negative exponent is now a positive exponent. Regarding the fractional exponent, if the expression were telling you to cube, then the 3 would be in the numerator, but the 3 is in the denominator, so, you are supposed to take ...
With a negative number inside the root, you cannot take the root if it is even (the denominator of the fraction), but it if it is odd, then the answer will end up negative. 7776 = 6^5 (rather than going through factoring, I did 7776^(1/5) in calculator), so squaring we end up with (-6)^2 which ends up as 36.
Simplifying Fractions With Negative Exponents Lesson. To best understand this lesson, make sure that you have read and understand the following lessons: Simplifying Negative Exponents; Simplifying Variables with Negative Exponents; This lesson will explain how to simplify the negative exponents in problems like the following two.
Welcome to Fractions with Exponents with Mr. J! Need help with how to solve a fraction with an exponent? You're in the right place!Whether you're just starti...
When we have a negative fraction as the power, we take the reciprocal because its the reversal of it. So a ^ (-1/2), would be 1 / sqrt(a). That means a/b ^ (-1/2) would be sqrt(b/a).
$\begingroup$ Yes, because you're adding a positive fraction to a negative number. You can certainly write $-(2\frac 12) = -(2 + \frac 12) -2 - \frac 12$, if that's what you want. Just use the parentheses to make it explicit that you want the negative of all of $2\frac 12$ $\endgroup$ –
