Question 237878
Until you get comfortable with exponents and the rules for working with them, one way to do problems like this is to rewrite the expression without the exponents:
{{{(-5x^5y^6)^3}}}
{{{(-5x^5y^6)(-5x^5y^6)(-5x^5y^6)}}}
{{{(-5*x*x*x*x*x*y*y*y*y*y*y)(-5*x*x*x*x*x*y*y*y*y*y*y)(-5*x*x*x*x*x*y*y*y*y*y*y)}}}
Now we can use the Commutative and Associative Properties to rearrange and regroup the "like" factors:
{{{((-5)*(-5)*(-5))(x*x*x*x*x*x*x*x*x*x*x*x*x*x*x)(y*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y)}}}
And then we simplify each group by multiplying out the numbers and rewriting the variables using exponents. Since -5*-5*-5 = -125 we get:
{{{-125x^15y^18}}}<br>
A shorter way, that you will learn eventually, is to use the properties of exponents effectively. Since {{{(-5x^5y^6)}}} is a single term (you have to have additions and/or subtractions to have more than one term), you can use the property:
{{{(a*b)^p = a^p*b^p}}}
I call this a pseudo-distributive property because it looks similar to the Distributive Property (but it's not). The property lets us "distribute" or apply the exponent outside the parentheses <i>to each factor of the one term expression inside the parentheses</i>. Using this on your expression we get:
{{{(-5)^3*(x^5)^3*(y^6)^3}}}
We can multiply out the -5, and we use another property of exponents, {{{(a^p)^q = a^(p*q)}}}, on the variables we get:
{{{-125*x^(5*3)*y^(6*3)}}}
{{{-125*x^15*y^18}}}