Use the power of quotient rule to rewrite the expression into a single exponent

Question

1. 10^-5/5^-5
2. (1/4)^-7 + (-2)^-7
3. (-15)^12/3^12
4. (- 6/5)^10 ÷ (- 3/2)^10

Answer 1

1.

10^-5/5^-5= (1/10^5}/{1/5^5)=

5^5 /10^5=5^5 /(2•5)^5=

5^5 /5^5•2^5=1/2^5=2^-5

2.

(1/4)^-7 + (-2)^-7=

4^7+1/(-2)^7=

4^7+1/(-1•2)^7= 4^7+1/(-1)^7•2^7 =

4^7+1/(-1)•2^7=4^7-1/2^7=

16384-1/128=16384-0.0078125=

16383.9921875

This cannot be written as a single exponent.

3.

(-15)^12/3^12 =(-1•5•3)^12/3^12=

(-1)^12•5•^12•3^12/3^12=

1•5^12=5^12

4.

(- 6/5)^10 ÷ (- 3/2)^10=

(-1.2)^10/(1.5)^10=

(-1.2/1.5)^10=(-12/15)^10=

(-3•4/3•5)^10=(-4/5)^10=

(-1•4/5)^10=(-1)^10•(4/5)^10=

1•(4/5)^10=(4/5)^10