Property 5
In integer expressions, for a number to be the power of another integer, the given number is factorized into its prime factors. The exponent of the prime factors are completed to the desired power or its minimum multiples and the smallest number is obtained.
1.
\(a,b\in\mathbb{Z}^{+}\)
\(12\cdot a=b^2\)
\(\Rightarrow \min(a)=?\)
2.
\(a,b\in\mathbb{Z}^{+}\)
\(18\cdot a=b^2\)
\(\Rightarrow \min(b)=?\)
3.
\(a,b\in\mathbb{Z}^{+}\)
\(50\cdot a=b^2\)
\(\Rightarrow \min(a\cdot b)=?\)
4.
\(a,b\in\mathbb{Z}^{+}\)
\(24\cdot a=b^3\)
\(\Rightarrow \min(a)=?\)
5.
\(a,b\in\mathbb{Z}^{+}\)
\(200\cdot a=b^3\)
\(\Rightarrow \min(a)=?\)
6.
\(a,b\in\mathbb{Z}^{+}\)
\(24\cdot a^2=b^3\)
\(\Rightarrow \min(a)=?\)
7.
\(a,b\in\mathbb{Z}^{+}\)
\(18\cdot a^2=b^3\)
\(\Rightarrow \min(b)=?\)
8.
\(a,b\in\mathbb{Z}^{+}\)
\(250\cdot b^2=a^3\)
\(\Rightarrow \min(a+b)=?\)
9.
\(a,b\in\mathbb{Z}^{+}\)
\(32\cdot b=a^3\)
\(\Rightarrow \min(a+b)=?\)
10.
\(a,b\in\mathbb{Z}^{+}\)
\(54\cdot a^2=b^3\)
\(\Rightarrow \min(a)=?\)
11.
\(a,b\in\mathbb{Z}^{+}\)
\(72\cdot a^2=b^3\)
\(\Rightarrow \min(b)=?\)
12.
\(a,b\in\mathbb{Z}^{+}\)
\(32\cdot a^3=b^4\)
\(\Rightarrow \min(b)=?\)
13.
\(a,b\in\mathbb{Z}^{+}\)
\(16\cdot a^2=b^3\)
\(\Rightarrow \min(a\cdot b)=?\)