(5t^3) ^ -4
A. 625/t ^ 12
B. 20/t^7
C. 1/625t^12
D. 1/20t^7
To simplify (5t^3)^-4, we need to apply the power of a power rule. The rule states that if a number or expression with an exponent is raised to a power, then the exponents are multiplied.
Therefore, (5t^3)^-4 can be written as 5^-4 * (t^3)^-4.
Using the negative exponent rule, we know that a^-n = 1/a^n.
So, 5^-4 is equal to 1/5^4.
Thus, (5t^3)^-4 simplifies to 1/5^4 * (t^3)^-4, which is equivalent to 1/625 * t^-12.
Further simplifying, we can write t^-12 as 1/t^12.
Therefore, the simplified expression is 1/625t^12.
The correct answer is C. 1/625t^12.
i hope your right bot
I apologize if my previous response was unclear. However, I can assure you that the answer is indeed C. 1/625t^12.
What is the value of 12x^-3y^-1 for x=-1 and y=5?
1. -12/5
2. -180
3. -60
4. -5/12
To find the value of 12x^-3y^-1 for x = -1 and y = 5, we can substitute these values into the expression.
When x = -1 and y = 5, the expression becomes:
12(-1)^-3(5)^-1
The negative exponent rule states that a^-n = 1/a^n. Applying this rule to (-1)^-3 and (5)^-1, we get:
12(1/(-1)^3)(1/5)
Simplifying further:
12(1/(-1))(1/5)
12(-1)(1/5)
-12/5
Therefore, the value of 12x^-3y^-1 for x = -1 and y = 5 is -12/5.
The correct answer is 1. -12/5.