How do i simplify it and then write the final expression with positive exponent

Wow. That's complicated.

I'll walk you through it though.

We're going to do this in three steps.

1. Simplify 7^1/3 * 7^5/3

When the base is the same, simply add/subtract the exponents.

7^1/3 * 7^5/3 = 7^6/3 = 7^2

Now we have the bottom simplified to 7^2, or 7^6/3

Now the overall equation is (7^2/3 / 7^6/3)^6

2.

When you're subtracting two numbers with exponents that have the same base, you simply subtract the exponents.

6 - 2 = 4

Now we're left with (7^4/3)^6

3.

When you have a base with an exponent, to the power of another exponent, you simply multiply the exponents.

4/3 * 6 = 24/3 = 8

The simplified form of the expression is 7^8. (This is your answer.)

Let me know if you have any other questions! :)

answer: h

step-by-step explanation:

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!