1. ## indices (possibly)

ok id really apppreciate not just the answer but how you do these step by step, im revising for my AS level exam on the 9th of january so any help many many thanks

X5/2 x (sqre root)X

NB: the 5/2 is a power and the square root in the brackets is simply square root of X

hope you understand...

2. $x^{\frac{5}{2}} \cdot \sqrt{x} = x^{\frac{5}{2}} \cdot x^{\frac{1}{2}} = x^3$

3. Hello, RubbishAtMaths!

Simplify: . $x^{\frac{5}{2}}\,\sqrt{x}$

Recall that: . $\sqrt{x} \,=\,x^{\frac{1}{2}}$

So the problem is: . $x^{\frac{5}{2}}\cdot x^{\frac{1}{2}}$

Can you finish it now?

4. when multiplying power fractions do you do this:

5/2 . 1/2

5+1=6

6/2 = 3

so X to the power of 3?

5. ## Mulitplying powers

Hello RubbishAtMaths
Originally Posted by RubbishAtMaths
when multiplying power fractions do you do this:

5/2 . 1/2

5+1=6

6/2 = 3

so X to the power of 3?
Yes, more or less. The rule you need to know is:

$x^a \times x^b = x^{a+b}$

So to multiply powers of the same base, add the powers together. Here, the base is
$x$, the powers are $a$ and $b$. You're multiplying $x^a$ by $x^b$, so add the powers together: $x^{a+b}$

In the problem you were solving, the powers were fractions, so you just add the fractions using the usual rules. So:

$x^{\frac{5}{2}} \times x^{\frac{1}{2}}=x^{\frac{5}{2} + \frac{1}{2}} = x^{\frac{5+1}{2}} = x^{\frac{6}{2}} = x^3$