Bool type and exponents questions

[football52]

I'm pushing my knowledge on this program and so far so good but I came across 2 errors. Program Calculates the area of a rectangle or triangle, or the volume of a pyramid or cube.

The first error says there are two things wrong with it and says:
Error 1 error C2451: conditional expression of type 'std::basic_string<char,std::char_traits<char>,std::allocator<char>>' is illegal c:\users\cody\documents\visual studio 2013\projects\areavolumecalc\source.cpp 19 1 AreaVolumeCalc

2 IntelliSense: expression must have bool type (or be convertible to bool) c:\Users\Cody\Documents\Visual Studio 2013\Projects\AreaVolumeCalc\Source.cpp 19 6 AreaVolumeCalc

int main()
{
	//Get area or volume

	string areaVolume = "";
	cout << "Are you trying to find the area or volume?\n";
	cin >> areaVolume;
	
	//If area, ask rectangle or triangle

	if (areaVolume = "area")
	{
		string shapeArea = "";
		cout << "What shape is it? (Rectangle or Triangle)\n";
		cin >> shapeArea;

		//If rectangle ask for 2 values
		if (shapeArea == "rectangle")
		{
			double baseRectangle = 0;
			cout << "What is the base length?\n";
			cin >> baseRectangle;

			double heightRectangle = 0;
			cout << "What is the height?\n";
			cin >> heightRectangle;

			//Multiple 2 values together

			double rectangleProduct = (double)(baseRectangle * heightRectangle);

And then the other problem I am having is here with this error, I don't know the correct way to do the cube root of a number:

3 IntelliSense: expression must have integral or unscoped enum type c:\Users\Cody\Documents\Visual Studio 2013\Projects\AreaVolumeCalc\Source.cpp 108 25 AreaVolumeCalc

else
		{
			double baseCube = 0;
			cout << "What is the base length?\n";
			cin >> baseCube;

			//multiply base^3

			double cubeProduct = baseCube ^ 3;

[JLBorges]

// if (areaVolume = "area")
if ( areaVolume == "area" )

baseCube ^ 3 doesn't do what you expect it would do. http://en.wikipedia.org/wiki/Bitwise_operations_in_C

// double cubeProduct = baseCube ^ 3;
const double cubeProduct = baseCube * baseCube * baseCube ;