(Laws of Exponents with Integer Exponents MC)Which expression is equivalent to (8−2 • 35)−2?
Question
Which expression is equivalent to (8^{-2} • 3^{5})^{-2}
?
Solution
The expression (8−2 • 35)−2 can be simplified as follows:
Step 1: Perform the multiplication operation first according to the order of operations (PEMDAS/BODMAS), which states that multiplication and division should be performed before addition and subtraction.
So, 2 • 35 = 70.
Step 2: Substitute this value back into the expression to get:
8 - 70 = -62.
Step 3: Now, raise -62 to the power of -2.
The negative exponent rule states that a^-n = 1/a^n.
So, (-62)^-2 = 1/(-62)^2.
Step 4: Square -62 to get 3844.
So, 1/3844 is the simplified form of the given expression.
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