To simplify the expression [tex]\(\left(x^5\right)^{\frac{7}{10}}\)[/tex] and write the answer without parentheses, let's follow the steps straight through:
1. Understand the given expression: You are given [tex]\(\left(x^5\right)^{\frac{7}{10}}\)[/tex].
2. Use the power of a power property: When you raise a power to another power, you multiply the exponents. Mathematically, [tex]\(\left(a^m\right)^n = a^{mn}\)[/tex].
Applying this property to our expression, we get:
[tex]\[
\left(x^5\right)^{\frac{7}{10}} = x^{5 \cdot \frac{7}{10}}
\][/tex]
3. Multiply the exponents: Calculate the product of the exponents [tex]\(5\)[/tex] and [tex]\(\frac{7}{10}\)[/tex]:
[tex]\[
5 \cdot \frac{7}{10} = \frac{5 \cdot 7}{10} = \frac{35}{10} = 3.5
\][/tex]
4. Write the simplified result: After multiplying the exponents, we get:
[tex]\[
x^{3.5}
\][/tex]
Therefore, the simplified expression is:
\[
x^{3.5}
\
