3√3 is not equivalent to 9³/₄
3√3 is equivalent to [tex]9^\frac34[/tex]
step-by-step:
[tex]9^\frac34=(3^2)^\frac34=3^{2\cdot\frac34}=3^{\frac32}=3^{1+\frac12}=3^1\cdot3^\frac12=3\cdot\sqrt3=3\sqrt3[/tex]
The simplest form of the number [tex]9^\frac{3}{4}[/tex] is [tex]3 \ \sqrt[]{3}[/tex].
It is given that the [tex]9^\frac{3}{4}[/tex]
It is required to find the simplest value of [tex]9^\frac{3}{4}[/tex]
It is defined as the number if we multiply the number by itself we get the original number it is a non-negative number.
We have:
= [tex]9^\frac{3}{4}[/tex]
We can write the above number as below:
[tex]= (3^2)^\frac{3}{4}[/tex]
By the property of powers:
[tex]\rm (x^a)^b= x^a^\times ^b[/tex] , we get:
[tex]3^2^\times^\frac{3}{4} \\\\\\3^\frac{3}{2} \\\\\sqrt{3^3} \\\\\sqrt{3}\times \sqrt{3}\times\sqrt{3}\\\\3\sqrt{3}[/tex]
Thus, the simplest form of the number [tex]9^\frac{3}{4}[/tex] is [tex]3 \ \sqrt[]{3}[/tex].
Learn more about the square root of the numbers here:
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