Answer is 4 which order to solve? 3^0 (5^0 - 6^-1 * 3)/ 2^-1 I don't know if I should bring the 6^-1 down first or multiply by 3 first.

Jan 29, 2017

${3}^{0} \left(\frac{\left({5}^{0} - {6}^{- 1} \cdot 3\right)}{2} ^ \left(- 1\right)\right) = 1$

Explanation:

Following the order of operations, with the parentheses made explicit:

First, perform any operations within parentheses.

${3}^{0} \textcolor{red}{\left(\frac{\left({5}^{0} - {6}^{- 1} \cdot 3\right)}{2} ^ \left(- 1\right)\right)}$

Within those parentheses, we treat numerators and denominators as having parentheses around them, and so perform operations within those first.

$= {3}^{0} \left(\frac{\textcolor{red}{\left({5}^{0} - {6}^{- 1} \cdot 3\right)}}{2} ^ \left(- 1\right)\right)$

Evaluate any exponents. Recall that if $x \ne 0$, then ${x}^{0} = 1$ and that ${x}^{-} a = \frac{1}{x} ^ a$.

$= {3}^{0} \left(\frac{\left(\textcolor{red}{{5}^{0}} - {6}^{- 1} \cdot 3\right)}{2} ^ \left(- 1\right)\right)$

$= {3}^{0} \left(\frac{\left(1 - \textcolor{red}{{6}^{- 1}} \cdot 3\right)}{2} ^ \left(- 1\right)\right)$

$= {3}^{0} \left(\frac{\left(1 - \textcolor{red}{\frac{1}{6} ^ 1} \cdot 3\right)}{2} ^ \left(- 1\right)\right)$

$= {3}^{0} \left(\frac{\left(1 - \frac{1}{6} \cdot 3\right)}{2} ^ \left(- 1\right)\right)$

Perform any multiplication or division, going left to right.

$= {3}^{0} \left(\frac{\left(1 - \textcolor{red}{\frac{1}{6} \cdot 3}\right)}{2} ^ \left(- 1\right)\right)$

$= {3}^{0} \left(\frac{\left(1 - \textcolor{red}{\frac{3}{6}}\right)}{2} ^ \left(- 1\right)\right)$

$= {3}^{0} \left(\frac{\left(1 - \frac{1}{2}\right)}{2} ^ \left(- 1\right)\right)$

Perform any addition or subtraction, going left to right.

$= {3}^{0} \left(\frac{\left(\textcolor{red}{1 - \frac{1}{2}}\right)}{2} ^ \left(- 1\right)\right)$

$= {3}^{0} \left(\frac{\frac{1}{2}}{2} ^ \left(- 1\right)\right)$

All operations in the numerator have been completed. Moving to the denominator, we have an exponent to evaluate.

$= {3}^{0} \left(\frac{\frac{1}{2}}{\textcolor{red}{{2}^{- 1}}}\right)$

$= {3}^{0} \left(\frac{\frac{1}{2}}{\textcolor{red}{\frac{1}{2} ^ 1}}\right)$

$= {3}^{0} \left(\frac{\frac{1}{2}}{\frac{1}{2}}\right)$

We now perform the remaining division. Recall that any nonzero number divided by itself is $1$.

$= {3}^{0} \left(\textcolor{red}{\frac{\frac{1}{2}}{\frac{1}{2}}}\right)$

$= {3}^{0} \left(1\right)$

All operations within parentheses have been evaluated. Going back, we now evaluate the remaining exponents.

$= \textcolor{red}{{3}^{0}} \cdot 1$

$= 1 \cdot 1$

And finally, we perform the remaining multiplication.

$= 1$