Michael Doyle

Simplifying Expressions

BB-35
A) (2m3)(4m2)
B) 6y5/3y2
C) -4y2/6y7
D) (-2x2)3

A) When simplifying expression A, 2m3 and 4m2 have to be multiplied. In order to do this, the first thing to do is to check for like terms. m and m are like terms so they can be multiplied together resulting in 2m*4m=8m. Though, the original terms in this expression both have exponents. The law for multiplying with exponents is that whatever power each term is to, the exponential value is added together. So in this expression it would be m3+m2=m5. So when simplified, this expression is 8m5. Parenthesis is not needed anymore after multiplication.
B) When simplifying expression B, 6y5 is being divided by 3y2. Dividing terms with exponents is similar to multiplying, just the other way around. Rather than adding the power the each term is to, they are subtracted. Normal division is held for the rest of the terms. So, 6y/3y=2y. And since the exponents are being subtracted and not added, so it is y5-y2=y3. So when simplified, this expression is 2y3.
C) Expression C is very much similar to expression B, just with a negative term. The same rules apply as they always do, -4y/6y=-0.667y and for the exponents –y2-y7=-y-5. So the full expression simplified is -0.667-5.
D) For expression D, a term with and exponent is being put to the 3rd power. When this occurs, the exponential factors are multiplied. So the term -2x remains the same, but the 2 in -2x2 is multiplied by 3. Which then is seen as 2*3=6. Thus, the simplified expression is -2x6. Parenthesis is not needed anymore after multiplication.