Consider the geometric sequence 4, 40, 400, 4000, ... What is the next number?
2 answers:
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Before answering the exact question you sent, you have to understand one simple principle: there are two forms of a variable with a fraction as an exponent, exponential form and radical form.
Example:
![exponential\ form = x^{1/3}\\radical form = \sqrt[3]{x}](https://tex.z-dn.net/?f=exponential%5C%20form%20%3D%20x%5E%7B1%2F3%7D%5C%5Cradical%20form%20%3D%20%20%5Csqrt%5B3%5D%7Bx%7D%20)
If the exponent is a fraction, the denominator of the fraction is the number on the outside of the radical sign.
So, for #23, you would change![\sqrt[3]{a}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Ba%7D%20)
to 
. Then, because the a is the same after the 2 and the 3, you can add them up to get 
.
For #24, you'd do almost the same thing (change the radical-b's to
and 
. However, you can't add them up because the exponents are different (1/4 and 1/3), so you'd leave it as 
Example:
If the exponent is a fraction, the denominator of the fraction is the number on the outside of the radical sign.
So, for #23, you would change
For #24, you'd do almost the same thing (change the radical-b's to