Solve each equation. See Examples 4–6. x^2/3 = 4

검증된 단계별 안내

Start with the given equation: \(x^{2/3} = 4\).

To isolate \(x\), raise both sides of the equation to the reciprocal of the exponent \(\frac{2}{3}\), which is \(\frac{3}{2}\). This gives: \(\left(x^{2/3}\right)^{3/2} = 4^{3/2}\).

Simplify the left side using the power of a power property: \(x^{(2/3) \times (3/2)} = x^1 = x\).

Rewrite the right side \(4^{3/2}\) as \(\left(4^{1/2}\right)^3\), which means take the square root of 4 and then cube the result.

Calculate the right side step-by-step (square root of 4 is 2, then cube 2) to find the value of \(x\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Rational Exponents

Rational exponents represent roots and powers simultaneously. For example, x^(2/3) means the cube root of x squared, or (x^2)^(1/3). Understanding how to manipulate and interpret these exponents is essential for solving equations involving fractional powers.

Isolating the Variable

To solve equations, isolate the term containing the variable by performing inverse operations. In this case, you want to isolate x^(2/3) before applying further steps, which simplifies the process of solving for x.

Solving Radical Equations

Equations with rational exponents often require rewriting the expression as a radical and then raising both sides to an appropriate power to eliminate the root. This step helps to solve for the variable and check for extraneous solutions.

Solve each equation. See Examples 4–6. x2/3 = 4