In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 4^-1.5

검증된 단계별 안내

Recognize that the expression $4^{-1.5}$ involves a negative exponent, which means you will take the reciprocal of the base raised to the positive exponent. So, rewrite the expression as $\frac{1}{4^{1.5}}$.

Understand that the exponent $1.5$ can be expressed as a fraction: $1.5 = \frac{3}{2}$. This means you are dealing with a power of $4$ raised to $\frac{3}{2}$.

Rewrite $4^{\frac{3}{2}}$ using radicals: $4^{\frac{3}{2}} = \left(4^{\frac{1}{2}}\right)^3 = (\sqrt{4})^3$.

Calculate the square root of 4, which is $\sqrt{4} = 2$, and then raise this result to the third power: \$2^3$.

Finally, take the reciprocal of the result from the previous step to account for the negative exponent, giving you $4^{-1.5} = \frac{1}{2^3}$. Use a calculator to approximate this value and round to three decimal places.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

54s

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주요 개념

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

Exponents and Powers

Exponents indicate how many times a base number is multiplied by itself. A power like 4^-1.5 means raising 4 to the negative 1.5 exponent, which involves both a negative sign and a fractional exponent.

Negative Exponents

A negative exponent means taking the reciprocal of the base raised to the corresponding positive exponent. For example, 4^-1.5 equals 1 divided by 4^1.5, which changes the operation from multiplication to division.

Fractional Exponents and Roots

Fractional exponents represent roots and powers combined. An exponent of 1.5 equals 1 plus 0.5, so 4^1.5 is 4^1 times 4^0.5, or 4 times the square root of 4. Understanding this helps in calculating or approximating values.

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 4-1.5