Simplify each expression. Assume all variables are nonzero.
1.(-100s^3t^-5)/(25s^-2t^6)
A: (-4s^5)/(t^-11)
2. (16u^4v^6)^-2
A: ?
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Simplify the expression. Assume all variables represent nonzero
To simplify the expression (-100s^3t^-5)/(25s^-2t^6), we can follow these steps:
Step 1: Combine the numerators and denominators:
(-100s^3t^-5) divided by (25s^-2t^6)
Step 2: Simplify the base of each variable:
(-100s^3t^-5) divided by (25s^-2t^6)
(-100(s^3)/(t^-5))/(25(s^-2)/(t^6))
Step 3: Apply the laws of exponents:
The law of exponents for division states that when dividing terms with the same base, you subtract the exponents:
(-100s^3t^-5)/(25s^-2t^6)
=(-100s^3t^-5)*((s^2)/25)*((t^6)/1)
=(-4s^5)/(t^-11)
Therefore, the simplified expression is (-4s^5)/(t^-11).
For the second expression, (16u^4v^6)^-2, we can follow these steps:
Step 1: Apply the exponent to each term within the parentheses:
(16^(-2))*(u^(4*(-2)))*(v^(6*(-2)))
Step 2: Simplify the exponent and evaluate the powers:
(1/16^2) * (u^-8) * (v^-12)
(1/256) * (u^-8) * (v^-12)
Therefore, the simplified expression is (1/256) * (u^-8) * (v^-12).