Answer:
A
Step-by-step explanation:
So we have the equation:
[tex]3(x-4)^\frac{4}{3}+16=64[/tex]
First, let's subtract 16 from both sides:
[tex]3(x-4)^\frac{4}{3}=48[/tex]
Now, let's divide both sides by 3:
[tex](x-4)^\frac{4}{3}=16[/tex]
Remember that with fractional exponents, we can move the denominator into the root position. Therefore:
[tex](\sqrt[3]{x-4})^4=16[/tex]
Let's take the fourth root of both sides. Since we're taking an even root, make sure to have the plus-minus symbol!
[tex]\sqrt[3]{x-4} =\pm 2[/tex]
Cube both sides. Since we're cubing, the plus-minus stays.
[tex]x-4=\pm 8[/tex]
Add 4 to both sides.
[tex]x=\pm 8+4[/tex]
Calculator:
[tex]x=8+4\text{ or } x=-8+4\\x=12\text{ or } x=-4[/tex]
So, our answer is A.
And we're done!
