To simplify this expression, we can first combine the terms with the same base raised to different exponents.
We have [tex]0.6x^{\frac{1}{7}} \cdot 27^{\frac{2}{7}} \cdot 25^{\frac{4}{7}}[/tex]
Now, we know that [tex]27 = 3^3[/tex [tex]25 = 5^2[/tex]
Substitute these values into our expression [tex]0.6x^{\frac{1}{7}} \cdot (3^3)^{\frac{2}{7}} \cdot (5^2)^{\frac{4}{7}}[/tex]
Simplify the exponents [tex]0.6x^{\frac{1}{7}} \cdot 3^{\frac{6}{7}} \cdot 5^{\frac{8}{7}}[/tex]
Now, multiply the coefficients and combine the terms with the same base [tex]0.6 \cdot 3^{\frac{6}{7}} \cdot 5^{\frac{8}{7}} \cdot x^{\frac{1}{7}}[/tex]
Therefore, the simplified expression is [tex]0.6 \cdot 3^{\frac{6}{7}} \cdot 5^{\frac{8}{7}} \cdot x^{\frac{1}{7}}[/tex]
To simplify this expression, we can first combine the terms with the same base raised to different exponents.
We have
[tex]0.6x^{\frac{1}{7}} \cdot 27^{\frac{2}{7}} \cdot 25^{\frac{4}{7}}[/tex]
Now, we know that
[tex]27 = 3^3[/tex
[tex]25 = 5^2[/tex]
Substitute these values into our expression
[tex]0.6x^{\frac{1}{7}} \cdot (3^3)^{\frac{2}{7}} \cdot (5^2)^{\frac{4}{7}}[/tex]
Simplify the exponents
[tex]0.6x^{\frac{1}{7}} \cdot 3^{\frac{6}{7}} \cdot 5^{\frac{8}{7}}[/tex]
Now, multiply the coefficients and combine the terms with the same base
[tex]0.6 \cdot 3^{\frac{6}{7}} \cdot 5^{\frac{8}{7}} \cdot x^{\frac{1}{7}}[/tex]
Therefore, the simplified expression is
[tex]0.6 \cdot 3^{\frac{6}{7}} \cdot 5^{\frac{8}{7}} \cdot x^{\frac{1}{7}}[/tex]