Question
4.55. smplify each expression. b. \( \left(\frac{2}{3}\right)^{3} \) c. \( (2+3)^{8} \) a. \( 2\left(-\frac{1}{2}+\frac{1}{4}\right) \)
Ask by Carrillo Hanson. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a. –½
b. 8/27
c. 390625
Solution
We will simplify each expression one by one.
a. Simplify 2(–½ + ¼):
1. First, combine the terms in the parentheses. Find a common denominator for –½ and ¼. The common denominator is 4:
–½ = –2/4 and ¼ = 1/4.
2. So, (–2/4 + 1/4) = –1/4.
3. Multiply by 2:
2 × (–1/4) = –2/4 = –½.
b. Simplify (2/3)³:
1. Raise both the numerator and the denominator to the power of 3:
(2/3)³ = 2³/3³ = 8/27.
c. Simplify (2 + 3)⁸:
1. First, compute the addition inside the parentheses:
2 + 3 = 5.
2. Then raise 5 to the power of 8:
5⁸.
5⁸ = 390625.
So, the simplified answers are:
a. –½
b. 8/27
c. 390625
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Simplify this solution Bonus Knowledge
Let's break it down step by step! For \( a = 2\left(-\frac{1}{2}+\frac{1}{4}\right) \): First, simplify inside the parentheses: \(-\frac{1}{2} + \frac{1}{4} = -\frac{2}{4} + \frac{1}{4} = -\frac{1}{4}\). Now, multiply: \(2 \times -\frac{1}{4} = -\frac{1}{2}\). Now, for \( b = \left(\frac{2}{3}\right)^{3} \): This means \(\frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = \frac{2^3}{3^3} = \frac{8}{27}\). Finally, for \( c = (2+3)^{8} \): First, add \(2 + 3 = 5\), so it becomes \(5^8\). That’s \(390625\)! (A huge number, right?) So the simplified expressions are: a. \(-\frac{1}{2}\) b. \(\frac{8}{27}\) c. \(390625\)
