Find the length of a square with a perimeter of 48cmeter
2 answers:
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Answer:
Volume of rectangular prism =
Step-by-step explanation:
Given rectangular prism is made up of small cubes of volume 1 cubic centimeter.
To find volume of rectangular prism.
Solution:
Volume of rectangular prism is =
We know that all sides of a cube are equal in measure.
So, we will count the number of cubes on each side to get the exact measure.
Length side = 4 cubes = 5 cm
Width side = 2 cubes = 2 cm
Height side = 2 cubes = 2 cm
Thus volume of rectangular prism =
Volume of rectangular prism =
The main rule we use in this exercise is
and the more general case:
![( \sqrt[n]{a} ) ^{m} =( a^{ \frac{1}{n}} )^{m} = a^{ \frac{1}{n}*m}=a^{ \frac{m}{n}}](https://tex.z-dn.net/?f=%28%20%20%5Csqrt%5Bn%5D%7Ba%7D%20%20%29%20%5E%7Bm%7D%20%3D%28%20a%5E%7B%20%5Cfrac%7B1%7D%7Bn%7D%7D%20%29%5E%7Bm%7D%20%3D%20a%5E%7B%20%5Cfrac%7B1%7D%7Bn%7D%2Am%7D%3Da%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%7D)
Using these rules, we make all the indices, or exponents, look like
, and compare them to each other.
A.
B.
C.![( \sqrt[3]{125} ) ^{7} =( 125^{ \frac{1}{3}} )^{7} = 125^{ \frac{1}{3}*7}= 125^{ \frac{7}{3}}](https://tex.z-dn.net/?f=%28%20%20%5Csqrt%5B3%5D%7B125%7D%20%29%20%5E%7B7%7D%20%3D%28%20125%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%7D%20%29%5E%7B7%7D%20%3D%20125%5E%7B%20%20%5Cfrac%7B1%7D%7B3%7D%2A7%7D%3D%20125%5E%7B%20%5Cfrac%7B7%7D%7B3%7D%7D%20%20%20)
D.
and the more general case:
Using these rules, we make all the indices, or exponents, look like
A.
B.
C.
D.