tolong bantu jawab A sampai O terimaksih

Berikut ini adalah pertanyaan dari handriganteng pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Pertama

Tolong bantu jawab A sampai O terimaksih

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

a. a⁵ × a⁶ = a¹¹

b. a⁸ : a² = a⁶

c. (x⁵)³ = x¹⁵

d. (x³y⁴)⁵ = x¹⁵y²⁰

e. (2x³)⁴ = 16x¹²

f. (a⁵ × a³) × a² = a¹⁰

g. (a⁶ × a²) : a⁴ = a⁴

h. (a⁹ : a²) : a³ = a⁴

i. (x⁴)⁵ : x⁸ = x¹²

j. (x⁴y²)⁵ : (xy³)² = x¹⁸y⁴

k. 5u³v × 5²uv⁴ = 5³u⁴v⁵ atau 125u⁴v⁵

l. 6³pq × 6²p²q³ = 6⁵p³q⁴ atau 7.776p³q⁴

m. $\frac{\left ( \frac{5}{x} \right )^{13}}{\left ( \frac{5}{x} \right )^{8}}$ = $\frac{3.125}{x^{5}}$ atau $3.125x^{-5}$

n. $\frac{y^{2}t^{10}}{yt^{7}}$ = yt³

o. $\frac{3m^{2}n^{4}}{3mn^{2}}$ = mn²

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Pembahasan

Sebelum menjawab pertanyaan diatas, kalian harus perlu tahu terlebih dahulu sifat-sifat eksponen. Berikut sifat-sifatnya!

$\bf 1. \: a^{m} \times a^{n} = a^{m + n}$

$\bf 2. \: a^{m} \div a^{n} = a^{m - n}$

$\bf 3. \: (a^{m})^{n} = a^{m \times n}$

$\bf 4. \: (a \times b)^{m} = a^{m} \times b^{m}$

$\bf 5. \: (\frac{a}{b})^{m} = \frac{a^{m}}{b^{m}}$

$\bf 6. \: \frac{1}{a^{n}} = a^{-n}$

$\bf 7. \: \sqrt[n]{a^{m}} = a^{\frac{m}{n}}$

$\bf 8. \: a^{0} = 1$

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$\begin{aligned} \mathbf{a.)} \: a^{5} \times a^{6} & = a^{5 + 6} \\ & = a^{11} \end{aligned}$

$\begin{aligned} \mathbf{b.)} \: a^{8} \div a^{2} & = a^{8 - 2} \\ & = a^{6} \end{aligned}$

$\begin{aligned} \mathbf{c.)} \: (x^{5})^{3} & = x^{5 \times 3} \\ & = x^{15} \end{aligned}$

$\begin{aligned} \mathbf{d.)} \: (x^{3}y^{4})^{5} & = x^{3 \times 5} y^{4 \times 5} \\ & = x^{15}y^{20} \end{aligned}$

$\begin{aligned} \mathbf{e.)} \: (2x^{3})^{4} & = 2^{4} x^{3 \times 4} \\ & = 16x^{12} \end{aligned}$

$\begin{aligned} \mathbf{f.)} \: (a^{5} \times a^{3}) \times a^{2} & = (a^{5 + 3}) \times a^{2} \\ & = a^{8} \times a^{2} \\ & = a^{8 + 2} \\ & = a^{10} \end{aligned}$

$\begin{aligned} \mathbf{g.)} \: (a^{6} \times a^{2}) \div a^{4} & = (a^{6 + 2}) \div a^{4} \\ & = a^{8} \div a^{4} \\ & = a^{8 - 4}\\ & = a^{4} \end{aligned}$

$\begin{aligned} \mathbf{h.)} \: (a^{9} \div a^{2}) \div a^{3} & = (a^{9 - 2}) \div a^{3} \\ & = a^{7} \div a^{3} \\ & = a^{7 - 3} \\ & = a^{4} \end{aligned}$

$\begin{aligned} \mathbf{i.)} \: (x^{4})^{5} \div x^{8} & = x^{4 \times 5} \div x^{8} \\ & = x^{20} \div x^{8} \\ & = x^{20 - 8} \\ & = x^{12} \end{aligned}$

$\begin{aligned} \mathbf{j.)} \: (x^{4}y^{2})^{5} \div (xy^{3})^{2} & = x^{4 \times 5} y^{2 \times 5} \div x^{2} y^{3 \times 2} \\ & = x^{20} y^{10} \div x^{2} y^{6} \\ & = x^{20 - 2} y^{10 - 6} \\ & = x^{18}y^{4} \end{aligned}$

$\begin{aligned} \mathbf{k.)} \: 5u^{3}v \times 5^{2}uv^{4} & = 5^{1 + 2} u^{3 + 1} v^{1 + 4} \\ & = 5^{3}u^{4}v^{5} \\ & = 125u^{4}v^{5} \end{aligned}$

$\begin{aligned} \mathbf{l.)} \: 6^{3}pq \times 6^{2}p^{2}q^{3} & = 6^{3 + 2} p^{1 + 2} q^{1 + 3} \\ & = 6^{5}p^{3}q^{4} \\ & = 7.776p^{3}q^{4} \end{aligned}$

$\begin{aligned} \mathbf{m.)} \: \frac{\left ( \frac{5}{x} \right )^{13}}{\left ( \frac{5}{x} \right )^{8}} & = \frac{\frac{5^{13}}{x^{13}}}{\frac{5^{8}}{x^{8}}} \\ & = \frac{5^{13 - 8}}{x^{13 - 8}} \\ & = \frac{5^{5}}{x^{5}} \\ & = \frac{3.125}{x^{5}} \: \textrm{atau} \: 3.125x^{-5} \end{aligned}$