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]$$
\left(5xy^5\right)^2\left(y^3\right)^4,
$$[/tex]
follow these steps:
1. First, simplify [tex]$\left(5xy^5\right)^2$[/tex].
- The coefficient: [tex]$5^2 = 25$[/tex].
- The [tex]$x$[/tex] term: [tex]$x^2$[/tex].
- The [tex]$y$[/tex] term: [tex]$(y^5)^2 = y^{5 \cdot 2} = y^{10}$[/tex].
So,
[tex]$$
\left(5xy^5\right)^2 = 25x^2y^{10}.
$$[/tex]
2. Next, simplify [tex]$\left(y^3\right)^4$[/tex].
- Apply exponent multiplication to the [tex]$y$[/tex] term: [tex]$(y^3)^4 = y^{3 \cdot 4} = y^{12}$[/tex].
Thus,
[tex]$$
\left(y^3\right)^4 = y^{12}.
$$[/tex]
3. Now, multiply the two simplified expressions:
[tex]$$
25x^2y^{10} \cdot y^{12}.
$$[/tex]
- The coefficients multiply: [tex]$25 \cdot 1 = 25$[/tex].
- The [tex]$x$[/tex] term remains [tex]$x^2$[/tex].
- For the [tex]$y$[/tex] terms, add the exponents: [tex]$y^{10 + 12} = y^{22}$[/tex].
The overall expression becomes:
[tex]$$
25x^2y^{22}.
$$[/tex]
Among the provided answer choices, the correct simplification is
[tex]$$
\boxed{25x^2y^{22}}.
$$[/tex]
[tex]$$
\left(5xy^5\right)^2\left(y^3\right)^4,
$$[/tex]
follow these steps:
1. First, simplify [tex]$\left(5xy^5\right)^2$[/tex].
- The coefficient: [tex]$5^2 = 25$[/tex].
- The [tex]$x$[/tex] term: [tex]$x^2$[/tex].
- The [tex]$y$[/tex] term: [tex]$(y^5)^2 = y^{5 \cdot 2} = y^{10}$[/tex].
So,
[tex]$$
\left(5xy^5\right)^2 = 25x^2y^{10}.
$$[/tex]
2. Next, simplify [tex]$\left(y^3\right)^4$[/tex].
- Apply exponent multiplication to the [tex]$y$[/tex] term: [tex]$(y^3)^4 = y^{3 \cdot 4} = y^{12}$[/tex].
Thus,
[tex]$$
\left(y^3\right)^4 = y^{12}.
$$[/tex]
3. Now, multiply the two simplified expressions:
[tex]$$
25x^2y^{10} \cdot y^{12}.
$$[/tex]
- The coefficients multiply: [tex]$25 \cdot 1 = 25$[/tex].
- The [tex]$x$[/tex] term remains [tex]$x^2$[/tex].
- For the [tex]$y$[/tex] terms, add the exponents: [tex]$y^{10 + 12} = y^{22}$[/tex].
The overall expression becomes:
[tex]$$
25x^2y^{22}.
$$[/tex]
Among the provided answer choices, the correct simplification is
[tex]$$
\boxed{25x^2y^{22}}.
$$[/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
