Math Problem Statement

approximate 2 superscript 2.8

Solution

To approximate 22.82^{2.8}, you can use the property of exponents that states ab+c=ab×aca^{b+c} = a^b \times a^c. We can break down 2.82.8 as 2+0.82 + 0.8:

22.8=22+0.8=22×20.82^{2.8} = 2^{2+0.8} = 2^2 \times 2^{0.8}

We know that:

22=42^2 = 4

Now, we just need to approximate 20.82^{0.8}. One way to approximate 20.82^{0.8} is by using the binomial approximation or a calculator. If you use a calculator, you will find that:

20.81.7412^{0.8} \approx 1.741

Therefore:

22.8=4×1.7416.9642^{2.8} = 4 \times 1.741 \approx 6.964

So, 22.82^{2.8} is approximately 6.9646.964.

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Approximations

Formulas

a^(b+c) = a^b * a^c

Theorems

Properties of Exponents

Suitable Grade Level

Grades 9-12