Help with simplifying equations?

Question

I'm not very good at simplifying, and these 3 problems are giving me a tough time. If anyone can help it would be great:)

(c^3/d^4)^7

6x^2 / y^3 times y^ -2x^2 / 9x^2

12x^ -3 / y^4 times (y^ -2 x^2)^ -1 / 15x^ -2

Sorry its a little confusing to see, all of them are fractions. Any help AT ALL is great, thanks in advance

Answer 1

Hi,

(c^3/d^4)^7

Multiply the outside exponent times every inside exponent.

(c^3/d^4)^7 = c^21/d^28 <==ANSWER

6x^2 / y^3 times y^ -2x^2 / 9x^2

6x².....y^-2.x²

-----.X.----------- =

y³.........9x²

6x²........x²

-----.X.--------- =

y³.......9x²y²

6x²........1

-----.X.--------- =

y³.......9y²

6x²

------- <==ANSWER

9y^5

12x^ -3 / y^4 times (y^ -2 x^2)^ -1 / 15x^ -2

12x^-3.....(y^-2x^2)^-1

---------.X.------------------ =

y^4....... .....15x^-2

Multiply the outside exponent times every inside exponent inside the parentheses.

12x^-3.....y^2x^-2

---------.X.------------- =

y^4....... ..15x^-2

12... .......y^2

---------.X.------- =

x^3y^4.. ..15

4... .....1

------.X.---- =

x³y².. ..5

4

-------- <==ANSWER

5x³y²

I hope that helps!! :-)

Answer 2

1. (c^3/d^4)^7

*just multiply the exponents of c and d by 7

c^21/ d^28 ---- final answer

2. 6x^2 / y^3 times y^ -2x^2 / 9x^2

* transfer the "y" with the negative exponent to the denominator  

and remove the negative sign on the exponent

= (6x^2 / y^3)  X   (x^2/ 9x^2 y^ 2)

= (6x^2 / y^3)  X (1/9y^2)

= (6x^2) / (9y^5)

= 2x^2/ 3y^5------- final answer

3. 12x^ -3 / y^4 times (y^ -2 x^2)^ -1 / 15x^ -2

* again, transfer numbers with negative exponents

= (1/ 12x^ 3  y^4)  X  (15x^ 2/ (y^ -2 x^2)^ 1)

= (1/ 12x^ 3  y^4) X (15x^ 2 y^ 2 / x^2)

* cancel out like terms

=  (1/ 12x^ 3  y^4) X (15y^2)

= 15/12 x^ 3y^2

= 5/4x^ 3y^2------ final answer