Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To rewrite the expression [tex]\(3 y^{-\frac{4}{3}} \cdot 2 \sqrt[3]{y}\)[/tex] in the form [tex]\(k \cdot y^n\)[/tex], we start by breaking down and simplifying each component of the expression.
1. Rewrite each component in terms of an exponent:
The expression [tex]\(3 y^{-\frac{4}{3}}\)[/tex] is already in exponential form.
The term [tex]\(2 \sqrt[3]{y}\)[/tex] can be rewritten using exponents as [tex]\(2 y^{\frac{1}{3}}\)[/tex].
2. Combine the coefficients:
Multiply the numerical coefficients together:
[tex]\[ 3 \cdot 2 = 6 \][/tex]
3. Combine the exponents:
Add the exponents for [tex]\(y\)[/tex]:
[tex]\[ y^{-\frac{4}{3}} \cdot y^{\frac{1}{3}} \][/tex]
Recall that when multiplying terms with the same base, the exponents are added:
[tex]\[ -\frac{4}{3} + \frac{1}{3} = -\frac{4}{3} + \frac{1}{3} = -\frac{3}{3} = -1 \][/tex]
4. Simplified expression:
Putting it all together, we get:
[tex]\[ 3 y^{-\frac{4}{3}} \cdot 2 y^{\frac{1}{3}} = 6 y^{-1} \][/tex]
In another form, [tex]\(y^{-1}\)[/tex] is the same as [tex]\(\frac{1}{y}\)[/tex].
So, the expression can be rewritten as:
[tex]\[ 6 y^{-1} \][/tex]
or equivalently,
[tex]\[ \frac{6}{y} \][/tex]
1. Rewrite each component in terms of an exponent:
The expression [tex]\(3 y^{-\frac{4}{3}}\)[/tex] is already in exponential form.
The term [tex]\(2 \sqrt[3]{y}\)[/tex] can be rewritten using exponents as [tex]\(2 y^{\frac{1}{3}}\)[/tex].
2. Combine the coefficients:
Multiply the numerical coefficients together:
[tex]\[ 3 \cdot 2 = 6 \][/tex]
3. Combine the exponents:
Add the exponents for [tex]\(y\)[/tex]:
[tex]\[ y^{-\frac{4}{3}} \cdot y^{\frac{1}{3}} \][/tex]
Recall that when multiplying terms with the same base, the exponents are added:
[tex]\[ -\frac{4}{3} + \frac{1}{3} = -\frac{4}{3} + \frac{1}{3} = -\frac{3}{3} = -1 \][/tex]
4. Simplified expression:
Putting it all together, we get:
[tex]\[ 3 y^{-\frac{4}{3}} \cdot 2 y^{\frac{1}{3}} = 6 y^{-1} \][/tex]
In another form, [tex]\(y^{-1}\)[/tex] is the same as [tex]\(\frac{1}{y}\)[/tex].
So, the expression can be rewritten as:
[tex]\[ 6 y^{-1} \][/tex]
or equivalently,
[tex]\[ \frac{6}{y} \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.