Algebra - simplify

Question

-5x^3(2xy)^2

Answer 1

To solve this problems, the (2xy)^2 must first be simplified.

 

-5x^3(2xy)^2 will simplify to 4x^2y^2 because everything within the parentheses will be squared. The problem then looks like -5x³4x²y². Since everything is being multiplied, the equation can be simplified by combing like factors. The product of -5 and 4 will be -20 and the product of x³ and x² is x⁵ because the superscript numbers are added when exponents with common bases are multiplied together. The y² is left alone because no other exponent has y as a base. To easier demonstrate the simplification looks like

 

-5x³4x²y²    --------->-20x⁵y²   After like factors are combined.

 

I hope this helps.

Answer 2

So, Maggie, let's do this using order of operations.  Remember PEMDAS?  We have to do the (2xy)^2 first.  That is 2xy times 2xy (I'll use "times" instead of x to avoid confusion) for multiplication to avoid confusion).  If we reorder things, that's 2 times 2 times x times x times y times y.  

 

-5x^3 is -5 times x times x times x, right?

 

If we combine everything and group like terms, we have -5 times 2 times 2 times x times x times x times x times x times y times y.  How would we write that using exponents?