Algebra 1 9th grade evaluate the following expression (fraction) [1 - (-4)^3]^2 numerator the denominator is [5^2 - 2.6] I want to know if my answer is correct 25
To evaluate the given expression \(\frac{{[1 - (-4)^3]^2}}{{5^2 - 2.6}}\), we need to simplify both the numerator and denominator and then divide them.
First, let's simplify the numerator:
\([1 - (-4)^3]^2\)
= \([1 - (-64)]^2\) (since \((-4)^3 = -64\))
= \([1 + 64]^2\)
= \([65]^2\)
= \(65^2\)
= 4225
Now, let's simplify the denominator:
\(5^2 - 2.6\)
= \(25 - 2.6\)
= \(22.4\)
Finally, let's divide the simplified numerator by the simplified denominator:
\(\frac{{4225}}{{22.4}}\)
The rounded answer is approximately 188.6160714.
Therefore, your answer of 25 is not correct.
To evaluate the given expression, we first need to simplify the numerator and denominator separately.
Let's start with the numerator. The expression inside the square brackets is [1 - (-4)^3]. To simplify this, we need to evaluate the exponent first.
(-4)^3 means (-4) raised to the power of 3. This can be calculated as -4 * -4 * -4, which gives us -64.
So, the numerator becomes [1 - (-64)]. Simplifying further, we have [1 + 64] = 65.
Next, let's simplify the denominator. The expression inside the square brackets is [5^2 - 2.6].
5^2 means 5 raised to the power of 2, which is 5 * 5 = 25.
So, the denominator becomes [25 - 2.6]. Evaluating this further, we have [22.4].
Now, we can rewrite the fraction as 65/22.4.
To check if your answer of 25 is correct, we divide 65 by 22.4 using a calculator. If the result is 25, then your answer is correct.
Using a calculator, 65 divided by 22.4 is approximately 2.9018.
So, the correct value of the expression is approximately 2.9018, not 25.
To evaluate the expression, let's follow the order of operations (PEMDAS).
First, we'll simplify the numerator: [1 - (-4)^3].
To calculate (-4)^3, we raise (-4) to the power of 3: (-4)^3 = -4 * -4 * -4 = -64.
So the numerator becomes: [1 - (-64)].
Now, simplify the numerator further:
[1 - (-64)] = [1 + 64] = 65.
Moving on to the denominator: [5^2 - 2.6].
First, calculate 5 squared: 5^2 = 5 * 5 = 25.
So the denominator becomes: [25 - 2.6].
Next, simplify the denominator:
[25 - 2.6] = 22.4.
Now we can evaluate the entire expression: (numerator)/(denominator) = 65/22.4.
Calculating this fraction gives us:
65/22.4 ≈ 2.901786.
Therefore, your answer is not correct. The value of the expression is approximately 2.901786, not 25.