Question

30^0.8 * 6^0.2 : 5^-1.2 = все под корнем (578^2 - 480^2) = a^1.2 : a^1.7 при a = 4 помогите решить , буду благодарен

Answer 1

${30}^{0.8} \times {6}^{0.2} \div {5}^{ - 1.2} = {30}^{ \frac{4}{5} } \times {6}^{ \frac{1}{5} } \div {5}^{ - \frac{6}{5} } = \sqrt[5]{ {30}^{4} } \times \sqrt[5]{6} \times {5}^{ \frac{6}{5} } = \sqrt[5]{ {5}^{4} \times {6}^{4} \times 6 \times {5}^{6} } = \sqrt[5]{ {5}^{10} \times {6}^{5} } = {5}^{2} \times 6 = 25 \times 6 = 150$

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$\sqrt{ {578}^{2} - {480}^{2} } = \sqrt{(578 - 480)(578 + 480)} = \sqrt{98 \times 1058} = \sqrt{ {7}^{2} \times 2 \times {23}^{2} \times 2} = 7 \times 23 \times 2 = 322$

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${a}^{1.2} \div {a}^{1.7} = {a}^{ - 0.5} = {a}^{ - \frac{1}{2} } = \frac{1}{ \sqrt{a} } = \frac{1}{ \sqrt{4} } = \frac{1}{2} = 0.5$

Answer 2

Let's break down the problem into steps:

1. Evaluate the expression:

   Copy code
   30^0.8 * 6^0.2 : 5^-1.2
   

   We can simplify this as follows:

   scssCopy code
   30^0.8 * 6^0.2 / 5^1.2
   = (3*10)^0.8 * (2*3)^0.2 / 5^(1+0.2)
   = 3^0.8 * 10^0.8 * 3^0.2 * 2^0.2 / 5^1.2
   = (3^(0.8+0.2) * 2^(0.2)) / 5^1.2 * 10^0.8
   = 3 * 2^(0.2) / 5^(1.2) * 10^(0.8)
   ≈ 3.771
   

   Therefore, 30^0.8 * 6^0.2 : 5^-1.2 ≈ 3.771.

2. Evaluate the expression under the square root:

   scssCopy code
   578^2 - 480^2
   = (578 + 480) * (578 - 480)
   = 1058 * 98
   = 103684
   

   Therefore, sqrt(578^2 - 480^2) = sqrt(103684) = 322.

3. Evaluate the expression:

   lessCopy code
   a^1.2 : a^1.7
   = a^(1.2 - 1.7)
   = a^(-0.5)
   

   Substituting a = 4, we get 4^(-0.5) = 1/2sqrt(2).

Now we can put it all together:

lessCopy code
30^0.8 * 6^0.2 : 5^-1.2 = sqrt(578^2 - 480^2) / 4^(1.2/1.7)

3.771 = 322 / a^(0.5)
a^(0.5) = 322 / 3.771
a^(0.5) = 85.297
a = 85.297^2
a ≈ 7280.92

Therefore, a ≈ 7280.92.