Question

What is the monomial if a square of a monomial is:1 9/16 a12b6

Answer 1

Answer:

$1\dfrac{1}{4}a^6b^3$

Step-by-step explanation:

A square of a monomial is $1\dfrac{9}{16}a^{12}b^6$ that is $\dfrac{25}{16}a^{12}b^{6}$

Use properties of exponents:

$(a^m)^n=a^{mn}\\ \\\dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^m\\ \\a^mb^m=(ab)^m$

Note that

$\dfrac{25}{16}=\dfrac{5^2}{4^2}=\left(\dfrac{5}{4}\right)^2\\ \\a^{12}=a^{6\cdot 2}=(a^6)^2\\ \\b^6=b^{3\cdot 2}=(b^3)^2$

Then

$\dfrac{25}{16}a^{12}b^{6}=\left(\dfrac{5}{4}\right)^2\cdot (a^6)^2\cdot (b^{3})^2=\left(\dfrac{5}{4}a^6b^3\right)^2$

So, the monomial is

$\dfrac{5}{4}a^6b^3=1\dfrac{1}{4}a^6b^3$