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.
(7^-64)x(7^-150)/(7^-7)x(7^2)
= 7^(-64-150+7-2)
= 7^-209

so, t = -209
answer is= 209
and its wrong i don't understand how

t=

In(x)
----- -205
In(7)

(7^-64)x(7^-150)/(7^-7)x(7^2)=7^t

when multiplying powers with the same base, keep the base and add the exponents

Left Side = 7^(-64 -150 -7 + 2)
= 7^-209

so we have:
7^-209 = t^t
clearly t = -209

If the text has an answer of +209, it is wrong.
Do you perhaps have a typo, such as 7^-t ?

To solve this equation, you need to understand exponent rules and how to simplify expressions with negative exponents. Let's break it down step by step:

Step 1: Simplify the expression on the left side of the equation using exponent rules:
(7^-64) * (7^-150) / (7^-7) * (7^2)

To multiply numbers with the same base, you add the exponents:
7^(-64 - 150) / 7^(-7 + 2)

Since the dividing numbers have the same base, you subtract the exponents:
7^(-214) / 7^(-5)

Now, we have a division of numbers with the same base, so subtract the exponents:
7^(-214 - (-5))
7^(-214 + 5)
7^(-209)

So, the expression simplifies to 7^(-209).

Step 2: Now, the equation is 7^(-209) = 7^t.

To solve for t, we can equate the exponents:
-209 = t

Therefore, the value of t in the given equation is -209.

It seems there was a mistake in your calculation of the final exponent. The correct value for t is -209.