Question

Simplify the given expression to rational exponent form, justify each step by identifying the properties of rational exponents used. All work must be shown.
1 over the cube root of the quantity of x to the negative sixth power

Answer 1

Here are the rules: x^3 is short for x*x*x a^5 is short for a*a*a*a*a in general, the exponent (little number in the upper right) tells you how many times to multiply the big number by itself.people expanded that idea by noticing this pattern: b^1 = b b^2 = b*b b^3 = b*b*b if you go "backwards" to b^0 what do you get? There is a way to make a good guess... and it says b^0 is 1 and b^(-1) is 1/b and b^(-2) is 1/(b*b) the negative exponents are the "flipped" version of the positive exponents.after working out what negative exponents, 0, and positive exponents mean, people extended the idea to fractional exponents. they decided that b^(½) means the square root b^(⅓) means the cube root b^(¼) means the fourth root.

Answer 2

@mathgal1108

Answer 3

first step is use this idea b^(⅓) means the cube root in other words, we can get rid of the cube root sign and replace it with an exponent ⅓ instead.it will look like this

Answer 4

now use the rule (a^b)^c = a^(bc) in other words, you can simplify the exponents to -6*⅓ = -2
you get 1/(x^(-2)) now you can use a rule to write x^(-2) as 1/x^2 and you get 1 divided by 1/x^2 which is the same as x^2 or in general, if you have 1/x^-2 then flip it and change the sign of the exponent 1/x^-2 becomes x^2

Answer 5

@TheOcean Thank you so much! I like that you explained it! Its much clearer now, thank you!

Answer 6

no probem anytime.