algebra

i need help to simplify with positive exponents only.

(b^2)^-6/b^-4

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

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  2. yes

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  3. 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.

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