SOLUTION: Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. {{{(3x^10y^9)^3}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. {{{(3x^10y^9)^3}}}       Log On


   

Question 373644: Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression.
%283x%5E10y%5E9%29%5E3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%5E10y%5E9%29%5E3
For this problem we will be using the rule for exponents: %28a%2Ab%29%5Eq+=+a%5Eq%2Ab%5Eq. Before we start however, a couple of comments:
  • If you have trouble remembering the rules for exponents or if you have trouble figuring out which rule for exponent to use, write the expression without exponents and simplify it this way.
  • The property mentioned above can easily be misused. It is critical to understand that this property only applies when the expression in the parentheses is just a single term. It does not apply to an expression that has more than one term. For example, the rule does not apply to %28a%2Bb%29%5Eq

Using the property on your expression we get:
%283%29%5E3%2A%28x%5E10%29%5E3%2A%28y%5E9%29%5E3
3%5E3+=+27. For the rest we will use another rule for exponents: %28a%5Ep%29%5Eq+=+a%5E%28p%2Aq%29:
27%2Ax%5E%2810%2A3%29%2Ay%5E%289%2A3%29
which simplifies to:
27%2Ax%5E30%2Ay%5E27