evaluate the exponential expression. write your answer as a fraction in simplest form.
1) ( 5 to the power of 3) to the power of -1
2)12 to the power of -2
1) 1/5^3 = 1/125
2) 1/(12)^2 = 1/144
1) (5^3)^-1 = 5^(3*-1) = 5^(-3)
So, the answer is 1/5^3 = 1/125.
2) 12^(-2) = 1/12^2 = 1/144.
Therefore, the answer is 1/144.
To evaluate the exponential expressions and write the answers as fractions in simplest form, we can follow these steps:
1) (5 to the power of 3) to the power of -1:
First, we solve the expression within the parentheses: 5 to the power of 3, which means multiplying 5 by itself three times.
5 to the power of 3 = 5 * 5 * 5 = 125.
Now, we apply the exponent -1 to the result from the previous step. To raise a number to a negative exponent, we can take the reciprocal or inverse of the number. In this case, we take the reciprocal of 125.
Reciprocal of 125 = 1/125.
The final answer to the first expression is 1/125.
2) 12 to the power of -2:
This means we need to multiply 12 by itself two times and then take the reciprocal or inverse of the result.
12 to the power of -2 = 1 / (12 * 12) = 1 / 144.
The final answer to the second expression is 1/144.