We appreciate your visit to Choose the correct simplification of the expression tex left 5 x y 5 right 2 left y 3 right 4 tex A tex 25 x. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To simplify the expression [tex]\((5xy^5)^2(y^3)^4\)[/tex], let's go through it step by step:
1. Simplify [tex]\((5xy^5)^2\)[/tex]:
- When you raise a power to another power, you multiply the exponents.
- For the coefficient [tex]\(5\)[/tex]: [tex]\((5)^2 = 25\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(x^1\)[/tex] becomes [tex]\(x^2\)[/tex] after applying the power.
- For [tex]\(y^5\)[/tex]: [tex]\((y^5)^2 = y^{5 \times 2} = y^{10}\)[/tex].
- So, [tex]\((5xy^5)^2 = 25x^2y^{10}\)[/tex].
2. Simplify [tex]\((y^3)^4\)[/tex]:
- Applying the power rule, [tex]\((y^3)^4 = y^{3 \times 4} = y^{12}\)[/tex].
3. Combine the simplified expressions:
- Now, multiply the two results: [tex]\(25x^2y^{10} \times y^{12}\)[/tex].
- Keep the coefficient: [tex]\(25\)[/tex].
- Since there is no other [tex]\(x\)[/tex] term, [tex]\(x^2\)[/tex] stays the same.
- For [tex]\(y\)[/tex], apply the rule of multiplying powers with the same base, which is to add the exponents: [tex]\(y^{10} \times y^{12} = y^{10 + 12} = y^{22}\)[/tex].
Putting it all together, the simplified expression is:
[tex]\[ 25x^2y^{22} \][/tex]
So, the correct answer is [tex]\(25 x^2 y^{22}\)[/tex].
1. Simplify [tex]\((5xy^5)^2\)[/tex]:
- When you raise a power to another power, you multiply the exponents.
- For the coefficient [tex]\(5\)[/tex]: [tex]\((5)^2 = 25\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(x^1\)[/tex] becomes [tex]\(x^2\)[/tex] after applying the power.
- For [tex]\(y^5\)[/tex]: [tex]\((y^5)^2 = y^{5 \times 2} = y^{10}\)[/tex].
- So, [tex]\((5xy^5)^2 = 25x^2y^{10}\)[/tex].
2. Simplify [tex]\((y^3)^4\)[/tex]:
- Applying the power rule, [tex]\((y^3)^4 = y^{3 \times 4} = y^{12}\)[/tex].
3. Combine the simplified expressions:
- Now, multiply the two results: [tex]\(25x^2y^{10} \times y^{12}\)[/tex].
- Keep the coefficient: [tex]\(25\)[/tex].
- Since there is no other [tex]\(x\)[/tex] term, [tex]\(x^2\)[/tex] stays the same.
- For [tex]\(y\)[/tex], apply the rule of multiplying powers with the same base, which is to add the exponents: [tex]\(y^{10} \times y^{12} = y^{10 + 12} = y^{22}\)[/tex].
Putting it all together, the simplified expression is:
[tex]\[ 25x^2y^{22} \][/tex]
So, the correct answer is [tex]\(25 x^2 y^{22}\)[/tex].
Thanks for taking the time to read Choose the correct simplification of the expression tex left 5 x y 5 right 2 left y 3 right 4 tex A tex 25 x. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
