Question

Skrng bikin kuis sendiri:
Sederhanakanlah tiap nomor:

[tex]\displaystyle(a.)\:\:\sqrt[3]{9} \cdot \sqrt[3]{3} \div 3^{-2}=....\\\\(b.)\:\:\sqrt{\sqrt{\sqrt{\sqrt{256}}}}=....\\\\(c.)\:\:\frac{a^b}{c^b}\cdot\frac{c^{-d}}{a^{-d}}=....[/tex]

Answer 1

a

[tex] = \sqrt[3]{9} \: . \: \sqrt[3]{3} \div {3}^{ - 2} [/tex]

[tex] = \sqrt[3]{ {3}^{2} } \: . \: \sqrt[3]{3} \div {3}^{ - 2} [/tex]

[tex] = {3}^{ \frac{2}{3} } \: . \: {3}^{ \frac{1}{3} } \div {3}^{ - 2} [/tex]

[tex] = {3}^{ \frac{2}{3} + \frac{1}{3} - ( - 2)} [/tex]

[tex] = {3}^{ \frac{3}{3} + 2} [/tex]

[tex] = {3}^{1 + 2} [/tex]

[tex] = {3}^{3} [/tex]

[tex] = 27[/tex]

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b

[tex] = \sqrt{ \sqrt{ \sqrt{ \sqrt{256} } } } [/tex]

[tex] = \sqrt{ \sqrt{ \sqrt{ \sqrt{ {2}^{8} } } } } [/tex]

[tex] = \sqrt{ \sqrt{ \sqrt{ {2}^{ \frac{8}{2} } } } } [/tex]

[tex] = \sqrt{ \sqrt{ {2}^{ \frac{8}{4} } } } [/tex]

[tex] = \sqrt{ {2}^{ \frac{8}{8} } } [/tex]

[tex] = \sqrt{2} [/tex]

[tex] = {2}^{ \frac{1}{2} } [/tex]

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c

[tex] = \frac{a^b}{c^b}\cdot\frac{c^{-d}}{a^{-d}}[/tex]

[tex] = \frac{ {a}^{b} {c}^{ - d} }{ {a}^{ - d} {c}^{b} } [/tex]

[tex] = {a}^{b - ( - d)} {c}^{ - d - b} [/tex]

[tex] = {a}^{b + d} {c}^{ - (b + d)} [/tex]