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Giải bài 8 trang 9 sách bài tập toán 11 - Chân trời sáng tạo tập 2

Rút gọn các biểu thức sau:

ꦇTổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Rút gọn các biểu thức sau: a) \({2^{\sqrt 3  + 1}}:{2^{\sqrt 3  - 1}}\); b) \({\left( {{3^{\sqrt 2 }}} \right)^{\sqrt 8 }}\); c) \({\left[ {{{\left( {\sqrt 7 } \right)}^{\sqrt 2 }}} \right]^{\sqrt 8 }}\); d) \({a^{2\sqrt 5  + 1}}:{a^{2\sqrt 5  - 2}}\); e) \({3^{3 + \sqrt 2 }}{.3^{ - 1 + \sqrt 2 }}{.9^{1 - \sqrt 2 }}\); g) \({\left( {{a^{ - \sqrt 3 }}.{b^{\frac{1}{{\sqrt 3 }}}}} \right)^{\frac{1}{{\sqrt 3 }}}}\).

Phương pháp giải - Xem chi tiết

Sử dụng các công thức về phép tính lũy thừa để tính: a, d) \(\frac{{{a^\alpha }}}{{{a^\beta }}} = {a^{\alpha  - \beta }}\) b, c) \({\left( {{a^\alpha }} \right)^\beta } = {a^{\alpha \beta }}\) e) \({a^\alpha }.{a^\beta } = {a^{\alpha  + \beta }}\), \({\left( {{a^\alpha }} \right)^\beta } = {a^{\alpha \beta }}\) g) \({\left( {a.b} \right)^\alpha } = {a^\alpha }.{b^\alpha }\)

Lời giải chi tiết

a) \({2^{\sqrt 3  + 1}}:{2^{\sqrt 3  - 1}} = {2^{\sqrt 3  + 1 - \sqrt 3  + 1}} = {2^2} = 4\); b) \({\left( {{3^{\sqrt 2 }}} \right)^{\sqrt 8 }} = {3^{\sqrt 2 .\sqrt 8 }} = {3^4} = 81\); c) \({\left[ {{{\left( {\sqrt 7 } \right)}^{\sqrt 2 }}} \right]^{\sqrt 8 }} = {\left( {\sqrt 7 } \right)^{\sqrt 2 .\sqrt 8 }} = {\left( {\sqrt 7 } \right)^4} = 49\); d) \({a^{2\sqrt 5  + 1}}:{a^{2\sqrt 5  - 2}} = {a^{2\sqrt 5  + 1 - 2\sqrt 5  + 2}} = {a^3}\); e) \({3^{3 + \sqrt 2 }}{.3^{ - 1 + \sqrt 2 }}{.9^{1 - \sqrt 2 }} = {3^{3 + \sqrt 2  +  - 1 + \sqrt 2 }}{.3^{2\left( {1 - \sqrt 2 } \right)}} = {3^{2 + 2\sqrt 2 }}{.3^{2 - 2\sqrt 2 }} = {3^{2 + 2\sqrt 2  + 2 - 2\sqrt 2 }} = {3^4} = 81\); g) \({\left( {{a^{ - \sqrt 3 }}.{b^{\frac{1}{{\sqrt 3 }}}}} \right)^{\frac{1}{{\sqrt 3 }}}} = {a^{ - \sqrt 3 .\frac{1}{{\sqrt 3 }}}}.{b^{\frac{1}{{\sqrt 3 }}.\frac{1}{{\sqrt 3 }}}} = \frac{1}{a}.{b^{\frac{1}{3}}} = \frac{{\sqrt[3]{b}}}{a}\).

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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