Question
write in exponential form: \( 1.1 \sqrt[3]{x^{2}} \) \( 1.2 \sqrt[4]{x^{5} y^{6}} \) \( 3.5 \sqrt[4]{x^{1}} \)
Ask by Garza Stephens. in South Africa
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Here are the expressions in exponential form:
1. \(1.1 \cdot x^{2/3}\)
2. \(1.2 \cdot x^{5/4} \cdot y^{3/2}\)
3. \(3.5 \cdot x^{1/4}\)
Solution
Sure, let's convert each expression from radical form to exponential form by using the property that \(\sqrt[n]{a} = a^{1/n}\).
1. **Expression:** \( 1.1 \sqrt[3]{x^{2}} \)
**Exponential Form:**
\[
1.1 \cdot x^{\frac{2}{3}}
\]
2. **Expression:** \( 1.2 \sqrt[4]{x^{5} y^{6}} \)
**Exponential Form:**
\[
1.2 \cdot x^{\frac{5}{4}} \cdot y^{\frac{6}{4}} = 1.2 \cdot x^{\frac{5}{4}} \cdot y^{\frac{3}{2}}
\]
3. **Expression:** \( 3.5 \sqrt[4]{x^{1}} \)
**Exponential Form:**
\[
3.5 \cdot x^{\frac{1}{4}}
\]
So, all three expressions in exponential form are:
1. \(1.1 \cdot x^{2/3}\)
2. \(1.2 \cdot x^{5/4} \cdot y^{3/2}\)
3. \(3.5 \cdot x^{1/4}\)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To express the given terms in exponential form, we need to remember that \( \sqrt[n]{a^m} = a^{m/n} \). For \( 1.1 \sqrt[3]{x^{2}} \): This can be rewritten as \( 1.1 (x^{2})^{1/3} = 1.1 x^{2/3} \). For \( 1.2 \sqrt[4]{x^{5} y^{6}} \): This is \( 1.2 (x^{5} y^{6})^{1/4} = 1.2 x^{5/4} y^{6/4} = 1.2 x^{5/4} y^{3/2} \). For \( 3.5 \sqrt[4]{x^{1}} \): This simplifies to \( 3.5 (x^{1})^{1/4} = 3.5 x^{1/4} \). So, in exponential form, the expressions are: 1. \( 1.1 x^{2/3} \) 2. \( 1.2 x^{5/4} y^{3/2} \) 3. \( 3.5 x^{1/4} \)
