Question

What does the exponent in an expression indicate?

Ask by Martinez Owen. in Indonesia
Feb 04,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

In a mathematical expression, the exponent shows how many times a number (the base) is multiplied by itself. It indicates the number of times the base is used as a factor. For example, in \(3^4\), the base is 3 and the exponent is 4, meaning 3 is multiplied by itself 4 times: \(3 \times 3 \times 3 \times 3 = 81\).

Solution

Dalam sebuah ekspresi matematika, eksponen menunjukkan berapa kali suatu bilangan (disebut basis) dikalikan dengan dirinya sendiri. Eksponen menandakan jumlah pengulangan perkalian tersebut. Misalnya, dalam ekspresi \(3^4\): - **Basis**: 3 - **Eksponen**: 4 Ekspresi \(3^4\) berarti 3 dikalikan dengan dirinya sendiri sebanyak 4 kali: \[ 3 \times 3 \times 3 \times 3 = 81 \] Eksponen juga digunakan untuk menyederhanakan penulisan bilangan yang sangat besar atau sangat kecil, serta dalam berbagai bidang matematika dan ilmu pengetahuan lainnya, seperti aljabar, kalkulus, dan fisika.

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The Deep Dive

The exponent in an expression indicates how many times the base is multiplied by itself. For example, in the expression \(2^3\), the base is 2, and the exponent is 3, meaning you multiply 2 by itself three times: \(2 \times 2 \times 2\), which equals 8. It’s a powerful shorthand that helps us manage large numbers and complex calculations efficiently! In the grand world of mathematics, exponents are also foundational for concepts like scientific notation, which expresses very large or very small numbers succinctly. For instance, instead of writing 0.000001, you can simply write \(1 \times 10^{-6}\). This makes calculations easier and reduces the risk of mistakes when dealing with extreme values, proving that exponents are not just a mathematical convenience, but a necessity in various fields like science, engineering, and finance!

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