## Tombrokaw 2 years ago What is the simplest way to do this? 49^-3/2

1. Tombrokaw

hello

2. Msky

Well, you can simplify $49^{-\frac{ 3 }{ 2 }}$ to $\left( 49^{\frac{ 1 }{ 2 }} \right)^{-3}$ And$49^{\frac{ 1 }{ 2 }}=\sqrt{49}=7$ so $\left( 49^{\frac{ 1 }{ 2 }} \right)^{-3}=\left( 7 \right)^{-3}=\frac{ 1 }{ 7\times7\times7 }$ This means that$49^{-\frac{ 3 }{ 2 }}=\frac{ 1 }{ 7\times7\times7 }$ If anything about this seems to complicated, let me know. The bottom line is that you're splitting the exponent into a power of 1/2 and a power of -3.

3. Tombrokaw

Yes I was able to get to the answer with help of another system actually but I thought it was too complicated and I was wondering if there was a much simpler way to do this?

4. Tombrokaw

In 49^1/2 . the denominator tells you if its a cube root or a square root or a quad root ?

5. CliffSedge

For fractional exponents, it's power-over-root.

6. Tombrokaw

Oh alright. Thank you. That clarifies it.