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
5. (-1.5)^3/(2.5)^-3
6. (5.6)^-14/4^14
(1/4)^-7 + (-2)^-7
(4^-1)^-7 + (-1)^-7 (2)^-7
4^7 - 2^-7
2^14 - 2^-7
(2^21 - 1)/2^7
there's no way to simplify that into a single power of 2
(-15)^12/3^12
(-1)^12 (3*5)^12 / 3^12
5^12
what do you get on the others?
OOBLECK AGAIN?
To rewrite the expressions using the quotient rule, we need to use the following property:
quotient rule: a^m / b^n = a^(m-n)
Now, let's rewrite the expressions one by one using the quotient rule:
1. 10^-5/5^-5
Using the quotient rule, we subtract the exponents: (-5) - (-5) = 0. Therefore, the expression simplifies to 10^0, which is equal to 1.
2. (1/4)^-7 + (-2)^-7
Applying the quotient rule, we subtract the exponents: (-7) - (-7) = 0. Therefore, the expression simplifies to (1/4)^0 + (-2)^0, which is equal to 1 + 1 = 2.
3. (-15)^12/3^12
Using the quotient rule, we subtract the exponents: 12 - 12 = 0. Therefore, the expression simplifies to (-15)^0, which is equal to 1.
4. (-6/5)^10 ÷ (-3/2)^10
Applying the quotient rule, we subtract the exponents: 10 - 10 = 0. Therefore, the expression simplifies to (-6/5)^0 ÷ (-3/2)^0, which is equal to 1 ÷ 1 = 1.
5. (-1.5)^3/(2.5)^-3
Using the quotient rule, we subtract the exponents: 3 - (-3) = 3 + 3 = 6. Therefore, the expression simplifies to (-1.5)^6/(2.5)^6.
6. (5.6)^-14/4^14
Applying the quotient rule, we subtract the exponents: (-14) - 14 = -28. Therefore, the expression simplifies to (5.6)^(-28)/4^(-28).
Please note that expressions involving negative exponents will result in fractions.