Answer:
[tex]\displaystyle 1)\ -\sqrt[3]{36}\\2)\ 10\sqrt[5]{10^{3}}\\3)\ 0.0016[/tex]
Step-by-step 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.
[tex]\displaystyle\sqrt[3]{-36}=\sqrt[3]{(-1)^3\cdot 2^2\cdot 3^2}=-\sqrt[3]{36}[/tex]
2.) 100 = 10², so ...
[tex]\displaystyle 100^{\frac{4}{5}}=10^{2\cdot\frac{4}{5}}=10^{1+\frac{3}{5}}=10\sqrt[5]{10^{3}}[/tex]
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.
