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

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

▪

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

▪

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