Question

How do you simplify each expression using positive exponent $ {({x^{ - 2}}{y^{ - 4}}{x^3})^{ - 2}} $ ?

Answer 1

Hint: To solve this we should know the basic difference between positive exponent and negative exponent.
Positive exponent is tell us how many number of time we have to multiply the base number and negative exponent is tell us that how many number if time we have to divide the base number.
 $ {x^{ - 2}} $ is a negative exponent to change to a positive exponent we write as $ \dfrac{1}{{{x^2}}} $ .

Complete step-by-step answer:
Step 1:
Calculate the power of each variable in the given exponent.
  $ {({x^{ - 2}}{y^{ - 4}}{x^3})^{ - 2}} = {x^4}{y^8}{x^{ - 6}} $
(By $ {({x^a})^b} = {x^{ab}} $ )
  $ \Rightarrow {x^4}{y^8}{x^{ - 6}} = {x^{4 - 6}}{y^8} $
  $ \Rightarrow {x^{4 - 6}}{y^8} = {x^{ - 2}}{y^8} $
Step 2:
Simplify this expression using positive exponent. We have to change the negative power of variables with positive by moving the numerator to denominator or vice-versa.
So,
 \[ \Rightarrow {x^{ - 2}}{y^8} = \dfrac{{{y^8}}}{{{x^2}}}\]
So, the correct answer is “ \[ {x^{ - 2}}{y^8} = \dfrac{{{y^8}}}{{{x^2}}}\]”.

Note: The best thing about exponential function is that it is useful in real world situations. Exponential functions are used in carbon data, to model population, help the coroner determine time of death, compute investment, and many other applications. The other names of exponents are index or power.