Ask Me Help Desk - Maths- Exponents

Evaluate 3 raised to 0 multiplied by 4 raised to 3/2.

First, do you know how to evaluate $3^0$ ?

Second, you can ealuate $4^{ \frac 3 2 }$ in either or two ways: this is equaivalent to either:

$ (4^3)^{\frac 1 2 } $

or

$ (4^{\small \frac 1 2 })^3 $

So to do this - do you know how to evaluate either of those expressions?

No... *** b more precise... I know that 3 raised to 0 stands for 1. can you explain the other half.

OK - a number raised to 1/2 means the square root of the number. If raised to 1/3 it's the cube root, etc. So for example:

$ 9^{1/2} = 3$ since $3^2 = 9$
$ 64^ {\small \frac 1 3} = 4$ since $4^3 = 64$

The other property of exponents to be aware of is that

$ a^{bc} = (a^b)^c = (a^c)^b $

Thus for example to evaluate $ 64^{\small \frac 2 3$ :

$ 64^{\small \frac 2 3 }= (64^{\small \frac 1 3 })^2 = 4^2 = 16$ , or you could do it like this:

$ 64^{\small \frac 2 3}= (64^2)^{\small \frac 1 3 } = 4096^{\small \frac 1 3} = 16$

Hope this helps.

Thank you very much... u helped clear my understanding completely...