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.
To simplify the given expression, (b^2)^-6 / b^-4, we can use the rule of exponents that states (a^m)^n = a^(m*n).
Step 1: Simplify the numerator
(b^2)^-6 = b^(2*-6) = b^-12
Step 2: Simplify the denominator
b^-4
To divide two terms with the same base, subtract the exponents:
b^-12 / b^-4 = b^(-12-(-4)) = b^-8
Step 3: Simplify the result
Since the exponent is negative, we can move the term to the denominator by changing the sign of the exponent:
b^-8 = 1 / b^8
So, the simplified expression is 1 / b^8.