algebra
posted by kate on .
i need help to simplify with positive exponents only.
(b^2)^6/b^4

Is it (b^2)^(6) all over b^(4)?

yes

When we have a power raised to another power, we multiply the powers.
(b^2)^(6) = b^(12)
Our problem is now b^(12) over b^(4).
Since the variable is the same, the variable with the largest power "wins."
If we have b^5 over b^2, that simplifies to b^3. We subtract the losing power (2) from the winning power (5).
In our case, the winning power is 4 because it is larger than 12. We subtract the loser from the winner: 4  (12) = 4 + 12 = 8.
We now have b^(8). To rewrite it with positive exponents only, we simply negate the power and flip it. 1 / b^8 is the final answer.
We can check this. Let b = 3.
(3^2)^(6) / 3^(4)
9^(6) / 3^(4)
Use your calculator.
1.52 x 10^(4)
1 / 3^8 is the same thing, so our answer is correct.