What is the value of t in the equation below?
(7^-64)x(7^-150)/(7^-7)x(7^2)=7^t
Help please i get lost when its a huge problem like this but if it's short i can solve it.
just add exponents when multiplying and subtract when dividing. So,
(7^-64)x(7^-150)/(7^-7)x(7^2)
= 7^(-64-150+7-2)
= 7^-209
so, t = -209
or, knowing that negative exponents mean that you swap places in the fraction, you have
7^7 / (6^64 * 7^150 * 7^2) = 1/7^209
its wrong
To find the value of t in the given equation (7^-64)x(7^-150)/(7^-7)x(7^2) = 7^t, we can simplify the equation by applying the rules of exponents and then equate the resulting expression with 7^t.
Let's break it down step by step:
Step 1: Apply the rule for multiplying exponents with the same base:
(7^-64) x (7^-150) = 7^(-64 - 150)
Step 2: Apply the rule for dividing exponents with the same base:
(7^(-64 - 150))/(7^-7) = 7^(-64 - 150 + 7)
Step 3: Apply the rule for multiplying exponents with the same base:
7^(-64 - 150 + 7) x (7^2) = 7^(-207 + 2)
Step 4: Simplify the exponents:
7^(-207 + 2) = 7^-205
Now, we have simplified the left side of the equation to 7^-205.
Step 5: Equate the simplified expression with 7^t:
7^-205 = 7^t
Since the bases are the same (7), the exponents must be equal. Therefore, t = -205.
So, the value of t in the given equation is -205.