Simplify the expression [ (2^(1/3) 8^(2/3) 6^(5/4) 3^(3/4)) / (9^-1 16^(1/3)) ] ^ -4

May 21, 2026Mathematics

ScanSolve AI Answer

May 21, 2026

Answer

2^3$

To find the value of $x$ , we need to simplify the expression using the rules of exponents.

The given expression is: $x = \left[\frac{2^{\frac{1}{3}} \times 8^{\frac{2}{3}} \times 6^{\frac{5}{4}} \times 3^{\frac{3}{4}}}{9^{-1} \times \sqrt[3]{16}}\right]^{-4}$

Step 1: Express all numbers as powers of their prime factors (2 and 3). $8 = 2^3$ $6 = 2 \times 3$ $9 = 3^2$ $\sqrt[3]{16} = 16^{\frac{1}{3}}

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To find the value of x, we need to simplify the expression using the rules of exponents.

Asked on May 21, 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 May 21, 2026

To find the value of x, we need to simplify the expression using the rules of exponents. The given expression is: x = [(2^1)/(3) × 8^(2)/(3) × 6^(5)/(4) × 3^(3)/(4)9^-1 × [3]16]^-4 Step 1: Express all numbers as powers of their prime factors (2 and 3). 8 = 2^3 6 = 2 × 3 9 = 3^2 $[3]16 = 16^(1)/(3)