Questions: Evaluate. [ frac-1-5^3+1(-3-2)^2 ]

$Evaluate. [ frac-1-5^3+1(-3-2)^2 ]$

Transcript text: Evaluate. \[ \frac{-1-5^{3}+1}{(-3-2)^{2}} \]

Solution

Solution Steps

To solve the given expression, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Evaluate the exponent in the numerator: $5^3$.
Perform the subtraction and addition in the numerator: $-1 - 5^3 + 1$.
Evaluate the expression inside the parentheses in the denominator: $-3 - 2$.
Evaluate the exponent in the denominator: $(-3 - 2)^2$.
Finally, divide the result of the numerator by the result of the denominator.

Step 1: Evaluate the Exponent in the Numerator

We start by calculating $5^3$: \[ 5^3 = 125 \]

Step 2: Calculate the Numerator

Next, we substitute the value of $5^3$ into the numerator: \[ \text{Numerator} = -1 - 125 + 1 = -125 \]

Step 3: Evaluate the Expression in the Denominator

Now, we evaluate the expression inside the parentheses: \[ -3 - 2 = -5 \]

Step 4: Calculate the Denominator

We then calculate the square of the result from the previous step: \[ \text{Denominator} = (-5)^2 = 25 \]

Step 5: Divide the Numerator by the Denominator

Finally, we divide the numerator by the denominator: \[ \text{Result} = \frac{-125}{25} = -5.0 \]

Final Answer

$\boxed{-5.0}$

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