Answer :
To express [tex]\( 3125x^{\frac{6}{5}} \)[/tex] in simplest radical form, let's break down the process step by step:
1. Factor the Constant:
- The number 3125 can be expressed in terms of powers. We know that [tex]\( 3125 = 5^5 \)[/tex].
2. Rewrite the Expression:
- The given expression is [tex]\( 3125x^{\frac{6}{5}} \)[/tex].
- Substitute [tex]\( 3125 \)[/tex] as [tex]\( 5^5 \)[/tex] to express the entire term with powers:
[tex]\[
5^5 \cdot x^{\frac{6}{5}}
\][/tex]
3. Simplify using Exponent Rules:
- We need to apply the laws of exponents to simplify the expression.
4. Convert to Radical Form:
- The expression [tex]\( x^{\frac{6}{5}} \)[/tex] can be rewritten in radical form. The exponent [tex]\(\frac{6}{5}\)[/tex] means:
[tex]\[
x^{\frac{6}{5}} = \left(x^{6}\right)^{\frac{1}{5}}
\][/tex]
- This implies taking the 5th root of [tex]\( x^6 \)[/tex].
5. Combining Terms:
- Therefore, we combine the factors and radical form:
[tex]\[
5^5 \cdot \sqrt[5]{x^6}
\][/tex]
This expression represents the original [tex]\(3125x^{\frac{6}{5}}\)[/tex] in simplest radical form.
1. Factor the Constant:
- The number 3125 can be expressed in terms of powers. We know that [tex]\( 3125 = 5^5 \)[/tex].
2. Rewrite the Expression:
- The given expression is [tex]\( 3125x^{\frac{6}{5}} \)[/tex].
- Substitute [tex]\( 3125 \)[/tex] as [tex]\( 5^5 \)[/tex] to express the entire term with powers:
[tex]\[
5^5 \cdot x^{\frac{6}{5}}
\][/tex]
3. Simplify using Exponent Rules:
- We need to apply the laws of exponents to simplify the expression.
4. Convert to Radical Form:
- The expression [tex]\( x^{\frac{6}{5}} \)[/tex] can be rewritten in radical form. The exponent [tex]\(\frac{6}{5}\)[/tex] means:
[tex]\[
x^{\frac{6}{5}} = \left(x^{6}\right)^{\frac{1}{5}}
\][/tex]
- This implies taking the 5th root of [tex]\( x^6 \)[/tex].
5. Combining Terms:
- Therefore, we combine the factors and radical form:
[tex]\[
5^5 \cdot \sqrt[5]{x^6}
\][/tex]
This expression represents the original [tex]\(3125x^{\frac{6}{5}}\)[/tex] in simplest radical form.
