For example, 2424 means 2∗2∗2∗22∗2∗2∗2. But what if your variable is being raised to a negative exponent? If you were given 2−42−4, how would you multiply two by itself negative four times? A negative exponent is equivalent to the inverse of the same number ...
2.10 Problems The material of which some scattering particles are made is assumed to have an absorption coefficient that is constant as a function of wavelength. For an ensemble of these particles whose size distribution follows a power law with a negative exponent [f (D) = kD−m, where k...
Example Problem 1: Using the Power of a Power Rule with Multivariate Expressions Simplify the following multivariate expression using the power of a power rule:(xy−3z4)−3 Step 1: Apply the power of a power rule Using the power of a power rule, we will multiply the exponent ...
Fractions and decimals can be converted to exponents, the superscript number that shows how many times the base number is multiplied to itself. Learn about exponents, and how negative exponents are unique through example practice problems.
Let and , we prove the nonexistence of positive stable solutions of weighted quasilinear problemThe result holds true for , or and , which is a positive critical exponent. Here and are nonnegative functions such that and for large |x|. We also construct an example to show the sharpness of...
Learn what an exponent is in math and how it is used. Identify the rules for and properties of exponents, and work through several exponents example problems. Related to this Question Simplify. Do not use negative exponents in the answer. \frac{9y^{-5{3y^{-11...
A negative exponent says how many times we have to divide the base number to get the desired result. Generally, negative numbers are used to represent very small numbers.Answer and Explanation: Negative numbers are used to represent very small numbers. For example, scientific notation uses ...
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We can rewrite (-3-4) using a positive exponent by taking the reciprocal of the base (-3) and applying the absolute value of the negative exponent (-4) to the denominator of the fraction like this: 1/(-3)4. Now we can simplify the denominator by evaluating (-3)4 which is the sa...
{u′(t,x)=Δu(t,x)+f(u(t,x))fort>0,x∈Ωu(0,x)=a(x)forx∈Ω. (RD) The partial differential equation in (RD) is an example of a reaction–diffusion equation. In addition to heat dynamics, these equations are used to model population genetics and many other processes in biol...