Problem: -18^ ?(-8)^18 = Does this answer look right? -18 ^ 8^9
P Panama New member Joined Nov 29, 2008 Messages 29 Dec 15, 2008 #1 Problem: -18^ ?(-8)^18 = Does this answer look right? -18 ^ 8^9
stapel Super Moderator Staff member Joined Feb 4, 2004 Messages 16,582 Dec 15, 2008 #2 Panama said: Problem: -18^ ?(-8)^18 = Click to expand... Assuming the instructions were to simplify, is the original expression as follows: . . . . .\(\displaystyle -18^{\sqrt{(-8)^{18}}}\) ...or is it something else? Thank you! Eliz.
Panama said: Problem: -18^ ?(-8)^18 = Click to expand... Assuming the instructions were to simplify, is the original expression as follows: . . . . .\(\displaystyle -18^{\sqrt{(-8)^{18}}}\) ...or is it something else? Thank you! Eliz.
P Panama New member Joined Nov 29, 2008 Messages 29 Dec 15, 2008 #3 The -18 on the left is suppose to be the index /root. But everything is is correct. Index..> -18^ sqrt(-8)^18
The -18 on the left is suppose to be the index /root. But everything is is correct. Index..> -18^ sqrt(-8)^18
L Loren Senior Member Joined Aug 28, 2007 Messages 1,299 Dec 15, 2008 #4 Are you saying \(\displaystyle -\sqrt[18]{-8}^{18}\) or \(\displaystyle \sqrt[-18]{-8}^{18}\) or \(\displaystyle -\sqrt[18]{(-8)^{18}}\) or something else?
Are you saying \(\displaystyle -\sqrt[18]{-8}^{18}\) or \(\displaystyle \sqrt[-18]{-8}^{18}\) or \(\displaystyle -\sqrt[18]{(-8)^{18}}\) or something else?
mmm4444bot Super Moderator Joined Oct 6, 2005 Messages 10,902 Dec 16, 2008 #6 \(\displaystyle -\sqrt[2]{(-8)^{2}}\;=\;-\sqrt[2]{(-8)(-8)}\;=\;-\sqrt[2]{8 \cdot 8}\;=\;-\sqrt[2]{64}\;=\;-8\) \(\displaystyle -\sqrt[4]{(-8)^{4}}\;=\;-\sqrt[4]{(-8)(-8)(-8)(-8)}\;=\;-\sqrt[4]{8 \cdot 8 \cdot 8 \cdot 8}\;=\;-\sqrt[4]{4096}\;=\;-8\) \(\displaystyle -\sqrt[6]{(-8)^{6}}\;=\;-\sqrt[6]{(-8)(-8)(-8)(-8)(-8)(-8)}\;=\;-\sqrt[6]{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}\;=\;-\sqrt[6]{262144}\;=\;-8\) \(\displaystyle -\sqrt[8]{(-8)^{8}}\;=\;-\sqrt[8]{(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)}\;=\;-\sqrt[8]{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}\;=\;-\sqrt[8]{16777216}\;=\;-8\) \(\displaystyle -\sqrt[10]{(-8)^{10}}\;=\;-\sqrt[10]{(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)}\;=\;-\sqrt[10]{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}\;=\;-\sqrt[10]{1073741824}\;=\;-8\) \(\displaystyle -\sqrt[12]{(-8)^{12}}\;=\;-\sqrt[12]{(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)}\;=\;-\sqrt[12]{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}\;=\;-\sqrt[12]{68719476736}\;=\;-8\) Do you notice a pattern?
\(\displaystyle -\sqrt[2]{(-8)^{2}}\;=\;-\sqrt[2]{(-8)(-8)}\;=\;-\sqrt[2]{8 \cdot 8}\;=\;-\sqrt[2]{64}\;=\;-8\) \(\displaystyle -\sqrt[4]{(-8)^{4}}\;=\;-\sqrt[4]{(-8)(-8)(-8)(-8)}\;=\;-\sqrt[4]{8 \cdot 8 \cdot 8 \cdot 8}\;=\;-\sqrt[4]{4096}\;=\;-8\) \(\displaystyle -\sqrt[6]{(-8)^{6}}\;=\;-\sqrt[6]{(-8)(-8)(-8)(-8)(-8)(-8)}\;=\;-\sqrt[6]{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}\;=\;-\sqrt[6]{262144}\;=\;-8\) \(\displaystyle -\sqrt[8]{(-8)^{8}}\;=\;-\sqrt[8]{(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)}\;=\;-\sqrt[8]{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}\;=\;-\sqrt[8]{16777216}\;=\;-8\) \(\displaystyle -\sqrt[10]{(-8)^{10}}\;=\;-\sqrt[10]{(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)}\;=\;-\sqrt[10]{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}\;=\;-\sqrt[10]{1073741824}\;=\;-8\) \(\displaystyle -\sqrt[12]{(-8)^{12}}\;=\;-\sqrt[12]{(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)(-8)}\;=\;-\sqrt[12]{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}\;=\;-\sqrt[12]{68719476736}\;=\;-8\) Do you notice a pattern?
P Panama New member Joined Nov 29, 2008 Messages 29 Dec 16, 2008 #7 The answer always becomes a -8? Is that the pattern you were speaking of?
D Denis Senior Member Joined Feb 17, 2004 Messages 1,707 Dec 16, 2008 #8 Panama, what is [sqrt(x)]^2 ? If you don't know that, you shouldn't even attempt this problem!
mmm4444bot Super Moderator Joined Oct 6, 2005 Messages 10,902 Dec 16, 2008 #9 Panama said: The answer always becomes a -8? Click to expand... Not always. Only when the index of the radical is both even and it matches the exponent on the radicand. EG \(\displaystyle - \sqrt[3]{(-8)^3} \; = \; - \sqrt[3]{(-8)(-8)(-8)} \; = \; - \sqrt[3]{-512} \; = \; -(-8) \; = \; 8\)
Panama said: The answer always becomes a -8? Click to expand... Not always. Only when the index of the radical is both even and it matches the exponent on the radicand. EG \(\displaystyle - \sqrt[3]{(-8)^3} \; = \; - \sqrt[3]{(-8)(-8)(-8)} \; = \; - \sqrt[3]{-512} \; = \; -(-8) \; = \; 8\)