Urgent help needed! Indices and fractions! 3s^1/2 x 5s^2

[Mathsdweeb000]

I understand indices fairly well but when using indices and fractions something always seems to go wrong. Here is an example problem that I do not get.

3s^1/2 x 5s^2

3s (only the s not the 3) to the power of 1/2 multiplied by 5s (only the s not the 5) to the power of 2

the answer in the book is 15s^5/2 (15 s to the power of 5/2)

My maths test is on Monday. Please help!

 

[Deleted member 4993]

I understand indices fairly well but when using indices and fractions something always seems to go wrong. Here is an example problem that I do not get.

3s^1/2 x 5s^2

3s (only the s not the 3) to the power of 1/2 multiplied by 5s (only the s not the 5) to the power of 2

the answer in the book is 15s^5/2 (15 s to the power of 5/2)

My maths test is on Monday. Please help!

Can you solve the following in fraction:

2 + 1/2 = ?

 

[stapel]

Here is an example problem that I do not get.

3s^1/2 x 5s^2

I will assume that the "x" is not a variable but here represents multiplication. Is the following the correct typesetting of the expression?

. . . . .\(\displaystyle 3s^{\frac{1}{2}}\, \times\, 5s^2\)

If so, kindly please clarify what you mean by "not getting" this exercise (which I'm assuming came with instructions to "simplify"). When you reply, please include a clear statement of your efforts so far. For instance, since everything here is multiplied, you started by grouping usefully:

. . . . .\(\displaystyle (3)\, (5)\, \left(s^{\frac{1}{2}}\right)\, \left(s^2\right)\)

You combined the constants, applied the exponent rule to the variable terms to convert the multiplied variables to one variable with added powers, and... then what?

Please be complete. Thank you!