We appreciate your visit to Simplify each expression Assume all variables are nonzero 45 tex frac 27 x 3 y 18 x 2 y 4 tex 46 tex left frac. 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 :
Sure! Let's simplify each expression step by step:
45. [tex]\(\frac{27 x^3 y}{18 x^2 y^4}\)[/tex]
1. Simplify the coefficients: [tex]\(\frac{27}{18} = \frac{3}{2}\)[/tex].
2. Simplify [tex]\(x\)[/tex] terms: [tex]\(x^3 / x^2 = x^{3-2} = x^1\)[/tex].
3. Simplify [tex]\(y\)[/tex] terms: [tex]\(y / y^4 = y^{1-4} = y^{-3}\)[/tex].
So, the simplified expression is: [tex]\(\frac{3}{2} x y^{-3}\)[/tex].
46. [tex]\(\left(\frac{3 a^3 b}{2 a^{-1} b^2}\right)^2\)[/tex]
1. Simplify the inside:
- Simplify [tex]\(a\)[/tex] terms: [tex]\(a^3 / a^{-1} = a^{3 - (-1)} = a^4\)[/tex].
- Simplify [tex]\(b\)[/tex] terms: [tex]\(b / b^2 = b^{1-2} = b^{-1}\)[/tex].
2. Simplifying the expression: [tex]\(\left(\frac{3 a^4 b^{-1}}{2}\right)^2 = \frac{(3^2 a^8 b^{-2})}{(2^2)} = \frac{9 a^8}{4 b^2}\)[/tex].
So, the simplified expression is: [tex]\(\frac{9 a^8}{4 b^2}\)[/tex].
47. [tex]\(12 a^0 b^5(-2 a^3 b^2)\)[/tex]
1. [tex]\(a^0\)[/tex] is 1 since anything raised to the zero power is 1.
2. Multiply the coefficients: [tex]\(12 \times (-2) = -24\)[/tex].
3. Multiply [tex]\(a\)[/tex] terms: [tex]\(a^0 \times a^3 = a^3\)[/tex].
4. Multiply [tex]\(b\)[/tex] terms: [tex]\(b^5 \times b^2 = b^{5+2} = b^7\)[/tex].
So, the simplified expression is: [tex]\(-24 a^3 b^7\)[/tex].
48. [tex]\(\frac{72 a^2 b^3}{-24 a^2 b^5}\)[/tex]
1. Simplify the coefficients: [tex]\(\frac{72}{-24} = -3\)[/tex].
2. Simplify [tex]\(a\)[/tex] terms: [tex]\(a^2 / a^2 = a^{2-2} = a^0\)[/tex], and since [tex]\(a^0 = 1\)[/tex], it simplifies out.
3. Simplify [tex]\(b\)[/tex] terms: [tex]\(b^3 / b^5 = b^{3-5} = b^{-2}\)[/tex].
So, the simplified expression is: [tex]\(-3 b^{-2}\)[/tex] or [tex]\(-\frac{3}{b^2}\)[/tex]
49. [tex]\(\left(\frac{5 m n}{-3 m^2}\right)^{-2}\)[/tex]
1. Simplify inside the parentheses: [tex]\(\frac{5}{-3} = -\frac{5}{3}\)[/tex].
2. Simplify [tex]\(m\)[/tex] terms: [tex]\(m / m^2 = m^{1-2} = m^{-1}\)[/tex].
3. Existing [tex]\(n\)[/tex] remains as [tex]\(n^1\)[/tex].
Now simplify: [tex]\(\left(-\frac{5 n m^{-1}}{3}\right)^{-2} = \left(-\frac{5 n}{3 m}\right)^{-2}\)[/tex].
4. Apply exponent rule: [tex]\(\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n\)[/tex].
So, it becomes [tex]\(\left(\frac{3 m}{5 n}\right)^2 = \frac{(3 m)^2}{(5 n)^2} = \frac{9 m^2}{25 n^2}\)[/tex].
50. [tex]\(6 x^5 y^3(-3 x^2 y^{-1})\)[/tex]
1. Multiply the coefficients: [tex]\(6 \times (-3) = -18\)[/tex].
2. Multiply [tex]\(x\)[/tex] terms: [tex]\(x^5 \times x^2 = x^{5+2} = x^7\)[/tex].
3. Multiply [tex]\(y\)[/tex] terms: [tex]\(y^3 \times y^{-1} = y^{3-1} = y^2\)[/tex].
So, the simplified expression is: [tex]\(-18 x^7 y^2\)[/tex].
I hope these steps are clear and help you understand how to simplify each expression!
45. [tex]\(\frac{27 x^3 y}{18 x^2 y^4}\)[/tex]
1. Simplify the coefficients: [tex]\(\frac{27}{18} = \frac{3}{2}\)[/tex].
2. Simplify [tex]\(x\)[/tex] terms: [tex]\(x^3 / x^2 = x^{3-2} = x^1\)[/tex].
3. Simplify [tex]\(y\)[/tex] terms: [tex]\(y / y^4 = y^{1-4} = y^{-3}\)[/tex].
So, the simplified expression is: [tex]\(\frac{3}{2} x y^{-3}\)[/tex].
46. [tex]\(\left(\frac{3 a^3 b}{2 a^{-1} b^2}\right)^2\)[/tex]
1. Simplify the inside:
- Simplify [tex]\(a\)[/tex] terms: [tex]\(a^3 / a^{-1} = a^{3 - (-1)} = a^4\)[/tex].
- Simplify [tex]\(b\)[/tex] terms: [tex]\(b / b^2 = b^{1-2} = b^{-1}\)[/tex].
2. Simplifying the expression: [tex]\(\left(\frac{3 a^4 b^{-1}}{2}\right)^2 = \frac{(3^2 a^8 b^{-2})}{(2^2)} = \frac{9 a^8}{4 b^2}\)[/tex].
So, the simplified expression is: [tex]\(\frac{9 a^8}{4 b^2}\)[/tex].
47. [tex]\(12 a^0 b^5(-2 a^3 b^2)\)[/tex]
1. [tex]\(a^0\)[/tex] is 1 since anything raised to the zero power is 1.
2. Multiply the coefficients: [tex]\(12 \times (-2) = -24\)[/tex].
3. Multiply [tex]\(a\)[/tex] terms: [tex]\(a^0 \times a^3 = a^3\)[/tex].
4. Multiply [tex]\(b\)[/tex] terms: [tex]\(b^5 \times b^2 = b^{5+2} = b^7\)[/tex].
So, the simplified expression is: [tex]\(-24 a^3 b^7\)[/tex].
48. [tex]\(\frac{72 a^2 b^3}{-24 a^2 b^5}\)[/tex]
1. Simplify the coefficients: [tex]\(\frac{72}{-24} = -3\)[/tex].
2. Simplify [tex]\(a\)[/tex] terms: [tex]\(a^2 / a^2 = a^{2-2} = a^0\)[/tex], and since [tex]\(a^0 = 1\)[/tex], it simplifies out.
3. Simplify [tex]\(b\)[/tex] terms: [tex]\(b^3 / b^5 = b^{3-5} = b^{-2}\)[/tex].
So, the simplified expression is: [tex]\(-3 b^{-2}\)[/tex] or [tex]\(-\frac{3}{b^2}\)[/tex]
49. [tex]\(\left(\frac{5 m n}{-3 m^2}\right)^{-2}\)[/tex]
1. Simplify inside the parentheses: [tex]\(\frac{5}{-3} = -\frac{5}{3}\)[/tex].
2. Simplify [tex]\(m\)[/tex] terms: [tex]\(m / m^2 = m^{1-2} = m^{-1}\)[/tex].
3. Existing [tex]\(n\)[/tex] remains as [tex]\(n^1\)[/tex].
Now simplify: [tex]\(\left(-\frac{5 n m^{-1}}{3}\right)^{-2} = \left(-\frac{5 n}{3 m}\right)^{-2}\)[/tex].
4. Apply exponent rule: [tex]\(\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n\)[/tex].
So, it becomes [tex]\(\left(\frac{3 m}{5 n}\right)^2 = \frac{(3 m)^2}{(5 n)^2} = \frac{9 m^2}{25 n^2}\)[/tex].
50. [tex]\(6 x^5 y^3(-3 x^2 y^{-1})\)[/tex]
1. Multiply the coefficients: [tex]\(6 \times (-3) = -18\)[/tex].
2. Multiply [tex]\(x\)[/tex] terms: [tex]\(x^5 \times x^2 = x^{5+2} = x^7\)[/tex].
3. Multiply [tex]\(y\)[/tex] terms: [tex]\(y^3 \times y^{-1} = y^{3-1} = y^2\)[/tex].
So, the simplified expression is: [tex]\(-18 x^7 y^2\)[/tex].
I hope these steps are clear and help you understand how to simplify each expression!
Thanks for taking the time to read Simplify each expression Assume all variables are nonzero 45 tex frac 27 x 3 y 18 x 2 y 4 tex 46 tex left frac. 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
