Answer:
![x(\sqrt[12]{x^5} )](https://tex.z-dn.net/?f=x%28%5Csqrt%5B12%5D%7Bx%5E5%7D%20%29)
Step-by-step explanation:
We need to remember 2 rules when doing these:
1. ![\sqrt[n]{x^a} =x^{\frac{a}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5Ea%7D%20%3Dx%5E%7B%5Cfrac%7Ba%7D%7Bn%7D%7D)
2. 
Using these 2 rules, we can simplify the product (steps shown below):
![\sqrt[3]{x^2} *\sqrt[4]{x^3} \\=x^{\frac{2}{3}}*x^{\frac{3}{4}}\\=x^{\frac{2}{3}+\frac{3}{4}}\\=x^{\frac{17}{12}}\\=x^{\frac{12}{12}+\frac{5}{12}}\\=x(x^{\frac{5}{12}})\\=x(\sqrt[12]{x^5} )](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E2%7D%20%2A%5Csqrt%5B4%5D%7Bx%5E3%7D%20%5C%5C%3Dx%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%2Ax%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%5C%5C%3Dx%5E%7B%5Cfrac%7B2%7D%7B3%7D%2B%5Cfrac%7B3%7D%7B4%7D%7D%5C%5C%3Dx%5E%7B%5Cfrac%7B17%7D%7B12%7D%7D%5C%5C%3Dx%5E%7B%5Cfrac%7B12%7D%7B12%7D%2B%5Cfrac%7B5%7D%7B12%7D%7D%5C%5C%3Dx%28x%5E%7B%5Cfrac%7B5%7D%7B12%7D%7D%29%5C%5C%3Dx%28%5Csqrt%5B12%5D%7Bx%5E5%7D%20%29)
Rearranging, we see that it is the third choice.
Answer:
10 in.
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of the 4 sides.
perimeter of rectangle = length + length + width + width
Opposite sides of a rectangle have the same length. Since one side measures 4 inches, the opposite side also measures 4 inches. Since one side measures 1 inch, the opposite side also measures 1 inch. There are two 4-inch sides and two 1-inch sides.
perimeter = 4 in. + 4 in. + 1 in. + 1 in.
perimeter = 10 in.
Answer:
C
Step-by-step explanation:
The expression given is a difference of cubes and factors as
a³ - b³ = (a - b)(a² + ab + b²)
8
= (2
)³ ⇒ a = 2
27
= (3y²)³ ⇒ b = 3y²
Hence 2 factors are
(2
- 3y²) and
((2
)² + (2
× 3y²) + (3y²)²)
= (4
+ 6
y² + 9
)
Hence the factored form of the expression is C