Evaluate the cube root of (343a3)/(b3).

July 20, 2026Mathematics

ScanSolve AI Answer

July 20, 2026

Answer

$\frac{7a}{b}$

Ili kutathmini usemi uliotolewa, tutatumia sifa za mizizi ya ujazo.

Step 1: Gawanya mzizi wa ujazo kwa nambari na denominator. $\sqrt[3]{\frac{343 a^3}{b^3}} = \frac{\sqrt[3]{343 a^3}}{\sqrt[3]{b^3}}$

Step 2: Tumia sifa ya mzizi wa ujazo kwa bidhaa, $\sqrt[3]{xy} = \sqrt[3]{x} \cdot \sqrt[3]{y}$ . $\frac{\sqrt[3]{343 a^3}}{\sqrt[3]{b^3}} = \frac{\sqrt[3]{343} \cdot \sqrt[3]{a^3}}{\sqrt[3]{b^3}}$

Step 3: Tafuta mzizi wa ujazo wa kila nambari na kigezo. Tunajua kuwa $7^3 = 343$ , hivyo $\sqrt[3]{343} = 7$ . Pia, $\sqrt[3]{x^3} = x$ . $\frac{7 \cdot a}{b}$

Step 4: Rahisisha usemi. $\frac{7a}{b}$

Jibu la mwisho ni: $\frac{7a{b}}$ Tuma swali linalofuata 📸

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Quick Answer

Ili kutathmini usemi uliotolewa, tutatumia sifa za mizizi ya ujazo.
3/(b^3) = [3]343 a^3[3]b^3 Step 2: Tumia sifa ya mzizi wa ujazo kwa bidhaa, [3]xy = [3]x · [3]y.
[3]343 a^3[3]b^3 = [3]343 · [3]a^3[3]b^3 Step 3: Tafuta mzizi wa ujazo wa kila nambari na kigezo.
Tunajua kuwa 7^3 = 343, hivyo [3]343 = 7.

Asked on July 20, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on July 20, 2026

Ili kutathmini usemi uliotolewa, tutatumia sifa za mizizi ya ujazo. Step 1: Gawanya mzizi wa ujazo kwa nambari na denominator. 3/(b^3) = [3]343 a^3[3]b^3 Step 2: Tumia sifa ya mzizi wa ujazo kwa bidhaa, [3]xy = [3]x · [3]y. [3]343 a^3[3]b^3 = [3]343 · [3]a^3[3]b^3 Step 3: Tafuta mzizi wa ujazo wa kila nambari na kigezo. Tunajua kuwa 7^3 = 343, hivyo [3]343 = 7. Pia, [3]x^3 = x. (7 · a)/(b) Step 4: Rahisisha usemi. (7a)/(b) Jibu la mwisho ni: (7a)/(b) Tuma swali linalofuata 📸