Use the power of quotient rule to rewrite the expression into a single exponent
1. 10^-5/5^-5
2. (1/4)^-7 + (-2)^-7
3. (-15)^12/3^12
4. (- 6/5)^10 ÷ (- 3/2)^10
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