Math Problem Statement

Solve the following tasks related to exponents and radicals: 1. Simplify the following exponential expressions: a. 9 * 10^6 * 10^-4 * 10^-7 b. 10^3 * 100^2 c. 5^3 * (1/25)^1 * 5^-2 d. (1/3)^5 : 9 2. Rationalize the following radical expressions: a. 10 / sqrt(5) b. 10 / (sqrt(3) + sqrt(8)) c. 20 / sqrt(10) d. 24 / (sqrt(13) - sqrt(7)) e. 15 / (sqrt(7) + sqrt(2)) f. 0 / sqrt(3)

Solution

The image contains a math assignment with two main tasks. Here's a transcription of the content:


Tugas Matematika

Pelajaran materi eksponen dan bentuk akar untuk persiapan STS minggu depan

Untuk pemantapan, silahkan kerjakan latihan berikut. Kerjakan dicatatan masing-masing dan kumpulkan sebagai bukti kehadiran.

  1. Ubahlah soal-soal di bawah menjadi bentuk pangkat paling sederhana: a. 91061041079 \cdot 10^6 \cdot 10^{-4} \cdot 10^{-7}

    b. 103100210^3 \cdot 100^2

    c. 53(125)1525^3 \cdot \left( \frac{1}{25} \right)^1 \cdot 5^{-2}

    d. (13)5:9\left( \frac{1}{3} \right)^5 : 9

  2. Rasionalkan bentuk akar berikut: a. 105\frac{10}{\sqrt{5}}

    b. 103+8\frac{10}{\sqrt{3} + \sqrt{8}}

    c. 2010\frac{20}{\sqrt{10}}

    d. 24137\frac{24}{\sqrt{13} - \sqrt{7}}

    e. 157+2\frac{15}{\sqrt{7} + \sqrt{2}}

    f. 03\frac{0}{\sqrt{3}}


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Math Problem Analysis

Mathematical Concepts

Exponents
Radicals
Simplification
Rationalization

Formulas

Laws of Exponents: a^m * a^n = a^(m+n), a^m / a^n = a^(m-n)
Rationalizing Denominators: multiply numerator and denominator by the conjugate of the denominator

Theorems

Exponentiation rules
Radical simplification and rationalization

Suitable Grade Level

Grades 9-12