The expressions are illustrations of rational exponent expressions
The equivalent expressions are [tex](8x)^\frac 12 = 2\sqrt{2x[/tex], [tex]6z^\frac 12 = 6\sqrt z[/tex] and [tex]\sqrt{19} = 19^\frac 12[/tex]
How to simplify the rational exponent expressions?
From the complete question (see attachment), we are to simplify or rewrite the following expressions
[tex](8x)^\frac 12[/tex]
[tex]6z^\frac 12[/tex]
[tex]\sqrt{19[/tex]
For [tex](8x)^\frac 12[/tex], we simply apply the exponent rule of indices
[tex](8x)^\frac 12 = \sqrt{8x[/tex]
Express 8 as 4 * 2
[tex](8x)^\frac 12 = \sqrt{4 * 2x[/tex]
Take the square root of 4
[tex](8x)^\frac 12 = 2\sqrt{2x[/tex]
For [tex]6z^\frac 12[/tex], we apply the exponent rule of indices
[tex]6z^\frac 12 = 6\sqrt z[/tex]
For [tex]\sqrt{19[/tex], we apply the the same rule
[tex]\sqrt{19} = 19^\frac 12[/tex]
Hence, the equivalent expressions are [tex](8x)^\frac 12 = 2\sqrt{2x[/tex], [tex]6z^\frac 12 = 6\sqrt z[/tex] and [tex]\sqrt{19} = 19^\frac 12[/tex]
Read more about rational exponents at:
https://brainly.com/question/535578
