SOLUTION: (3x ^2 yz ^3) ^2 (x^4y) ^3

Question 283873: (3x ^2 yz ^3) ^2 (x^4y) ^3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To simplify, we're going to use the following identities (equations that are true for all values of the given variable(s))

1. . Basically, you can either multiply first, then exponentiate, OR, exponentiate and then multiply. (note: this can expand to any number of terms inside the parenthesis. So you could have 50 terms in the parenthesis if you wanted). Example:

2. . When you raise an exponential expression to another exponent, you're going to multiply the exponents. Example:

3. . When you multiply monomials (with a common base), you're going to add the exponents. Example:

---------------------------------------

Let's use the identities shown above to simplify. I'll refer to each identity listed by the number associated with them.

Start with the given expression.

Use identity number 1 (see above) to break up the expression.

Use identity number 2.

Multiply

Group the terms with common bases (ie group all the 'x' terms together, etc.)

Use identity #3 to multiply the monomials.

Add

Square 3 to get

So simplifies to

In other words,
RELATED QUESTIONS
... (answered by checkley71)

(4x^4 z^2)^5 (x^3... (answered by stanbon,mandymae)

(3x^4y^3)^2 (answered by tommyt3rd)

Solve for x x=yz y=2 and... (answered by MathLover1)

Write {{{ln(x^2/yz^3)}}} in expanded... (answered by MathLover1)

3x^2y^3�3y^3�x^4y^2 (answered by Fombitz)

Which of the following is equivalent to x^4.yz^3/xyz^6 and explain how you got the... (answered by algebrahouse.com)

-3x -4y=2... (answered by TigerAlgebra)

3/4y=2/3x+1;(3,?) (answered by mananth)