Write each fraction as an expression using negative exponents: 2/3^2; a/b^6; f/g^3; 3m/n^2; d^2/d^3

Question

Write each fraction as an expression using negative exponents: 2/3^2; a/b^6; f/g^3 ; 3m/n^2; d^2/d^3

Answer 1

2/3^2; = 2/9 because the squaring can only apply to the denominator, w/o parentheses.

a/b^6; = ab^-6  because the exponent only applies to the denominator, there being no parentheses.

f/g^3 ; = fg^-3 because the exponent only applies to the denominator, there being no parentheses.

3m/n^2; = 3mn^-2 because the exponent only applies to the denominator, there being no parentheses.

d^2/d^3 = d^-1

 

NOW, IF THE FIRST PROBLEM, FOR EXAMPLE, HAS BEEN (2/3)² THEN THE ANSWER WOULD BE 4/9.

Answer 2

Anything under the fraction bar gets a negative exponent after simplifying.  

• 2/3^2=2(3)^-2
• a/b^6=a(b)^-6
• f/g^3=f(g)^-3
• 3m/n^2=3m(n)^-2
• Last one is a bit tricky, you need to simplify first.  You have 2 d's on top and 3 d's on bottom:(dd)/(ddd).  2 cancel out and you are left with one d on bottom. 
• d^2/d^3=1/d=(d)^-1

Answer 3

Use the fact that

 

(y / x)ⁿ = (x / y)^-n