The PowerSteps command is used to show the steps of simplifying exponents, logarithms and exponential function in a basic student expression.

If expr is a string, then it is parsed into an expression using InertForm:-Parse so that no automatic simplifications are applied, and thus no steps are missed.  

The fullsolution option can be used to show additional arithmetic steps in the simplification.

The displaystyle and output options can be used to change the output format.  See OutputStepsRecord for details.

This function is part of the Student:-Basics package.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right)\:$

$\mathrm{PowerSteps}\left(''2*75^(1/2)-5*27^(1/2)''\right)$

$\begin{array}{lll}& & \text{Let's simplify}\\ & & 2\cdot {75}^{\frac{1}{2}}-5\cdot {27}^{\frac{1}{2}}\\ \text{•}& & \text{Factor roots}\\ & & 2\cdot \left(5\cdot \sqrt{3}\right)-1\cdot \left(5\cdot \left(3\cdot \sqrt{3}\right)\right)\\ \text{•}& & \text{Multiply}2\cdot \left(5\sqrt{3}\right)\\ & & \left(10\sqrt{3}\right)-1\cdot \left(5\cdot \left(3\cdot 3^{\frac{1}{2}}\right)\right)\\ \text{•}& & \text{Multiply}5\cdot \left(3\sqrt{3}\right)\\ & & 10\sqrt{3}-\left(15\sqrt{3}\right)\\ \text{•}& & \text{Add}10\sqrt{3}-15\sqrt{3}\\ & & \left(-5\sqrt{3}\right)\end{array}$

$\mathrm{PowerSteps}\left(''(5)^(1/2)/(2*(10)^(1/2)*(2)^(1/2))''\right)$

$\begin{array}{lll}& & \text{Let's simplify}\\ & & \frac{5^{\frac{1}{2}}}{2\cdot {10}^{\frac{1}{2}}\cdot 2^{\frac{1}{2}}}\\ \text{•}& & \text{Multiply in order to rationalize the denominator}\\ & & \frac{\sqrt{10}\cdot \sqrt{2}}{\sqrt{10}\cdot \sqrt{2}}\cdot \left(\frac{\sqrt{5}}{2\sqrt{10}\sqrt{2}}\right)\\ \text{•}& & \text{Multiply the denominator}\\ & & \frac{\sqrt{10}\cdot \sqrt{2}\cdot \sqrt{5}}{40}\\ \text{•}& & \text{Factor roots}\\ & & \frac{\sqrt{2}\cdot \sqrt{5}\cdot \sqrt{2}\cdot \sqrt{5}}{40}\\ \text{•}& & \text{Combine}\left\{\sqrt{2}\cdot \sqrt{2}\,\sqrt{5}\cdot \sqrt{5}\right\}\\ & & \frac{2\cdot 5}{40}\\ \text{•}& & \text{Multiply}2\cdot 5\\ & & \frac{10}{40}\\ \text{•}& & \text{Cancel out factor of}10\\ & & \frac{1}{4}\end{array}$

$\mathrm{PowerSteps}\left(''(k^4)^(5*a)/(k^3*k^6)''\,\mathrm{output}=\mathrm{typeset}\right)$

$\begin{array}{lll}& & \text{Let's simplify}\\ & & \frac{{\left(k^4\right)}^{5\cdot a}}{k^3\cdot k^6}\\ \text{•}& & \text{Apply the integer power of a power rule,}{\left(a^n\right)}^m=a^{nm}\\ & & \frac{k^{4\cdot \left(5a\right)}}{k^3\cdot k^6}\\ \text{•}& & \text{Multiply}4\cdot \left(5a\right)\\ & & \frac{k^{\left(20a\right)}}{k^3\cdot k^6}\\ \text{•}& & \text{Apply the product rule}{a}^n{a}^m=a^{n+m}\text{to add exponents with common base}\\ & & \frac{k^{20a}}{k^{3+6}}\\ \text{•}& & \text{Add exponents}\\ & & \frac{k^{20a}}{k^9}\\ \text{•}& & \text{Divide}\\ & & k^{-9+20a}\end{array}$

The Student[Basics][PowerSteps] command was introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.