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how would i turn 1/2^-3 into a positive exponent?

 Apr 15, 2015

Best Answer 

 #2
avatar+26367 
+5

how would i turn 1/2^-3 into a positive exponent ?

$$\dfrac{1}{ 2^{-3} } = \left( \dfrac{1}{ 2 } \right)^{-3}\\\\
\small{\text{
Formula:
$\boxed{
\left( \dfrac{a}{b} \right)^{-3}
= \left( \dfrac{b}{a} \right)^{3}
}$}}\\\\
\left( \dfrac{1}{ 2 } \right)^{-3}
=\left( \dfrac{2}{ 1 } \right)^{3} = 2^3$$

 Apr 15, 2015
 #1
avatar+980 
+5

$${\frac{{\mathtt{1}}}{{{\mathtt{2}}}^{-{\mathtt{3}}}}}$$

$${\frac{\left({\frac{{\mathtt{1}}}{{\mathtt{1}}}}\right)}{\left({\frac{{\mathtt{1}}}{{{\mathtt{2}}}^{{\mathtt{3}}}}}\right)}}$$

$$\left({\frac{{\mathtt{1}}}{{\mathtt{1}}}}\right){\mathtt{\,\times\,}}\left({\frac{{{\mathtt{2}}}^{{\mathtt{3}}}}{{\mathtt{1}}}}\right)$$

$${{\mathtt{2}}}^{{\mathtt{3}}}$$

If you get used to doing this you can skip straight from $${\frac{{\mathtt{1}}}{{{\mathtt{2}}}^{-{\mathtt{3}}}}}$$ to $${{\mathtt{2}}}^{{\mathtt{3}}}$$

.
 Apr 15, 2015
 #2
avatar+26367 
+5
Best Answer

how would i turn 1/2^-3 into a positive exponent ?

$$\dfrac{1}{ 2^{-3} } = \left( \dfrac{1}{ 2 } \right)^{-3}\\\\
\small{\text{
Formula:
$\boxed{
\left( \dfrac{a}{b} \right)^{-3}
= \left( \dfrac{b}{a} \right)^{3}
}$}}\\\\
\left( \dfrac{1}{ 2 } \right)^{-3}
=\left( \dfrac{2}{ 1 } \right)^{3} = 2^3$$

heureka Apr 15, 2015

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