Question

1 - properties of exponents and order of operations

score on last attempt: 1.3 out of 2
score in gradebook: 1.3 out of 2
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use the order of operations to simplify each expression.
when needed, write the answer as a decimal accurate to 4 decimal places.

a. simplify \\(\frac{21 + 2^2}{2^3}\\).

\\(\frac{21 + 2^2}{2^3} = \\) enter an integer or decimal number

b. simplify \\(\frac{4 - 12 \div 3}{18 + 3(-5)}).

\\(\frac{4 - 12 \div 3}{18 + 3(-5)} = 0\\)

c. simplify \\(\frac{-3 + 6(10 - 5(3))}{5(-2) - 5}\\).

\\(\frac{-3 + 6(10 - 5(3))}{5(-2) - 5} = 2.2\\)

points possible: 2
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score on last attempt: 1.3. score in gradebook: 1.3
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Explanation:

Part a

Step1: Calculate exponents

First, calculate the exponents in the numerator and the denominator. For the numerator, \(2^2 = 4\), and for the denominator, \(2^3=8\). So the expression becomes \(\frac{21 + 4}{8}\).

Step2: Add in the numerator

Now, add the numbers in the numerator: \(21+4 = 25\). So the expression is now \(\frac{25}{8}\).

Step3: Divide

Divide \(25\) by \(8\): \(\frac{25}{8}=3.125\).

Step1: Do division and multiplication

In the numerator, \(12\div3 = 4\), so numerator is \(4 - 4=0\). In the denominator, \(3\times(- 5)=- 15\), so denominator is \(18+( - 15)=3\). Then \(\frac{0}{3}=0\).

Step1: Calculate inside the innermost parentheses

First, calculate \(5(3) = 15\) inside the parentheses in the numerator: \(10-15=-5\).

Step2: Multiply in the numerator

Then, \(6\times(-5)=-30\), so numerator becomes \(-3 + (-30)=-33\).

Step3: Calculate denominator

In the denominator, \(5\times(-2)=-10\), so denominator is \(-10-5=-15\).

Step4: Divide

Now, divide \(-33\) by \(-15\): \(\frac{-33}{-15} = 2.2\).

Answer:

\(3.125\)

Part b (already solved as 0, verification below)