Question

PLEASE HELP ME!!!

I will give you 50 points!!!
Explain all your work
solve and show as an radical
1.)(-36)^1/3
2.) 100^4/5
3.) 0.04^2
That's all I just need to understand what I need to do I can finish my other 20 questions on my own:)
Have a nice Day

Answer 1

`\displaystyle 1)\ -\sqrt[3]{36}\\2)\ 10\sqrt[5]{10^(3)}\\3)\ 0.0016`

Explanation:

1.) The 1/3 power is simply the cube root. 36 = 2²×3² has no cubes that can be factored out, but the cube root of -1 is -1, so that can be factored out.

`\displaystyle\sqrt[3]{-36}=\sqrt[3]{(-1)^3\cdot 2^2\cdot 3^2}=-\sqrt[3]{36}`

2.) 100 = 10², so ...

`\displaystyle 100^{(4)/(5)}=10^{2\cdot(4)/(5)}=10^{1+(3)/(5)}=10\sqrt[5]{10^(3)}`

3.) 0.04^2 = (0.04)×(0.04) = 0.0016

As with any mulitplication involving decimal fractions, the total number of decimal places in the product is the total of the numbers of decimal places in the multiplicands. Here, each factor has 2 decimal places, so the product has 2+2=4 decimal places.

You can also consider this to be (4×10⁻²)² = 4²×10⁻⁴ = 16×10⁻⁴ = 0.0016. Same idea, expressed using exponents instead of counting decimal places.