Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
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]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.