+72 12m7 x 5n8 x 4p4 How do i simplify it? I don't see how you can.
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20m5 x 6n4
+26376 12m7 x 5n8 x 4p4
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20m5 x 6n4
How do i simplify it? I don't see how you can.
\(\begin{array}{rcll} \dfrac{ 12m^7 \cdot 5n^8 \cdot 4p^4 }{ 20m^5 \cdot 6n^4 } &=& \dfrac{12\cdot 5 \cdot 4} {20\cdot 6} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& \dfrac{12\cdot 5 \cdot 4} {6\cdot 20} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& \dfrac{12}{6}\cdot \dfrac{5 \cdot 4}{20} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& \dfrac{12}{6}\cdot \dfrac{20}{20} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& 2\cdot 1 \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& 2\cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& 2\cdot \dfrac{m^7 }{m^5} \cdot \dfrac{ n^8 }{n^4 } \cdot p^4 \\\\ &=& 2\cdot (m^7\cdot m^{-5}) \cdot ( n^8 \cdot n^{-4})\cdot p^4 \\\\ &=& 2\cdot m^{7-5} \cdot n^{8-4}\cdot p^4 \\\\ \mathbf{\dfrac{ 12m^7 \cdot 5n^8 \cdot 4p^4 }{ 20m^5 \cdot 6n^4 } }&\mathbf{=}& \mathbf{2\cdot m^{2} \cdot n^{4}\cdot p^4 } \\\\ \mathbf{\dfrac{ 12m^7 \cdot 5n^8 \cdot 4p^4 }{ 20m^5 \cdot 6n^4 } }&\mathbf{=}& \mathbf{2\cdot m^{2} \cdot (n\cdot p)^4 } \\\\ \end{array}\)
+26376 12m7 x 5n8 x 4p4
_____________
20m5 x 6n4
How do i simplify it? I don't see how you can.
\(\begin{array}{rcll} \dfrac{ 12m^7 \cdot 5n^8 \cdot 4p^4 }{ 20m^5 \cdot 6n^4 } &=& \dfrac{12\cdot 5 \cdot 4} {20\cdot 6} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& \dfrac{12\cdot 5 \cdot 4} {6\cdot 20} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& \dfrac{12}{6}\cdot \dfrac{5 \cdot 4}{20} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& \dfrac{12}{6}\cdot \dfrac{20}{20} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& 2\cdot 1 \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& 2\cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& 2\cdot \dfrac{m^7 }{m^5} \cdot \dfrac{ n^8 }{n^4 } \cdot p^4 \\\\ &=& 2\cdot (m^7\cdot m^{-5}) \cdot ( n^8 \cdot n^{-4})\cdot p^4 \\\\ &=& 2\cdot m^{7-5} \cdot n^{8-4}\cdot p^4 \\\\ \mathbf{\dfrac{ 12m^7 \cdot 5n^8 \cdot 4p^4 }{ 20m^5 \cdot 6n^4 } }&\mathbf{=}& \mathbf{2\cdot m^{2} \cdot n^{4}\cdot p^4 } \\\\ \mathbf{\dfrac{ 12m^7 \cdot 5n^8 \cdot 4p^4 }{ 20m^5 \cdot 6n^4 } }&\mathbf{=}& \mathbf{2\cdot m^{2} \cdot (n\cdot p)^4 } \\\\ \end{array}\)
+72 woahhhhhh... Could you explain that a bit more simply please? You've made me confused, sorry
+26376 Could you explain that a bit more simply please?
Changing the order of factors does not change the product,
i.e. if a and b are two real numbers, then \( a \cdot b = b\cdot a\) .
\(\begin{array}{rcll} \dfrac{ 12m^7 \cdot 5n^8 \cdot 4p^4 }{ 20m^5 \cdot 6n^4 } &=& \dfrac{12\cdot 5 \cdot 4} {20\cdot 6} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& \dfrac{12\cdot 5 \cdot 4} {6\cdot 20} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& \dfrac{12}{6}\cdot \dfrac{5 \cdot 4}{20} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& \dfrac{12}{6}\cdot \dfrac{20}{20} \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \quad | \quad \dfrac{12}{6} = 2 \quad \dfrac{20}{20} = 1\\\\ &=& 2\cdot 1 \cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& 2\cdot \dfrac{ m^7 \cdot n^8 \cdot p^4 }{ m^5 \cdot n^4 } \\\\ &=& 2\cdot \dfrac{m^7 }{m^5} \cdot \dfrac{ n^8 }{n^4 } \cdot p^4 \end{array}\)
\(\boxed{~ \begin{array}{c} \text{Formula Quotient rule with same base:}\\ ~\frac{a^n} {a^m} = a^{n-m} \\ ~\text{Example:}\\ ~\frac{2^5}{ 2^3 } = 2^{5-3} = 2^2= 2\cdot 2 = 4 \end{array} ~}\)
\(\begin{array}{rcll} \dfrac{ 12m^7 \cdot 5n^8 \cdot 4p^4 }{ 20m^5 \cdot 6n^4 } &=& 2\cdot (m^7\cdot m^{-5}) \cdot ( n^8 \cdot n^{-4})\cdot p^4 \\\\ &=& 2\cdot m^{7-5} \cdot n^{8-4}\cdot p^4 \\\\ \mathbf{\dfrac{ 12m^7 \cdot 5n^8 \cdot 4p^4 }{ 20m^5 \cdot 6n^4 } }&\mathbf{=}& \mathbf{2\cdot m^{2} \cdot n^{4}\cdot p^4 } \\\\ \end{array}\)
\(\boxed{~ \begin{array}{c} \text{Formula Product rule with same exponent:}\\ ~a^n\cdot b^n = (a\cdot b)^{n} \\ ~\text{Example:}\\ ~3^2\cdot 4^2 =(3\cdot 4)^2 = 12^2 = 12\cdot 12 = 144 \end{array} ~}\)
\(\begin{array}{rcll} \mathbf{\dfrac{ 12m^7 \cdot 5n^8 \cdot 4p^4 }{ 20m^5 \cdot 6n^4 } }&\mathbf{=}& \mathbf{2\cdot m^{2} \cdot (n\cdot p)^4 } \\\\ \end{array}\)
