## anonymous 5 years ago simplyfy (x-9)^3/5=8 how do you solve the power to 3/5?

1. watchmath

Raise both sides to the 5/3 power (x-9)=8^(5/3)=32 x-9=32 x=41

2. anonymous

i dont understand still

3. anonymous

$\sqrt[5]{(x-9)^2} = (x-9)^{3/5}$

4. anonymous

sorry, should be $\sqrt[5]{(x-9)^{3}}$

5. anonymous

Now$[\sqrt[5]{(x-9)^{3}}]^{5} = [8]^5$ $(x-9)^3 = 8^5$ $\sqrt[3]{(x-9)^3} = \sqrt[3]{[8^5]}$ $x-9 = 8^{5/3}$

6. anonymous

$8^{5/3} = \sqrt[3]{32768} = 32$

7. anonymous

so x-9 = 32 add 9 both sides x-9+9=32+9 x=41 hope it helps!

8. anonymous

lets try this. rather than raising to the fifth power first, take the cube root of 8 first. the cube root of 8 is 2, and 2 to the fifth power is 32. much easier that way.