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QuestionCalculate (−343)43(-343)^{\frac{4}{3}}.

Studdy Solution

STEP 1

Assumptions1. We are asked to calculate (−343)43(-343)^{\frac{4}{3}} . The base of the exponent is -3433. The exponent is 43\frac{4}{3}

STEP 2

We can rewrite the expression as a radical expression. The denominator of the fraction in the exponent represents the root, and the numerator represents the power.(−343)4=(−343)4(-343)^{\frac{4}{}} = \sqrt[]{(-343)^4}

STEP 3

Now, calculate the power part first, which is (-343)^.
(−343)=(−343)×(−343)×(−343)×(−343)(-343)^ = (-343) \times (-343) \times (-343) \times (-343)

STEP 4

Calculate the value of (−343)4(-343)^4.
(−343)4=13,841,287,201(-343)^4 =13,841,287,201

STEP 5

Now that we have the value of (−343)4(-343)^4, we can substitute it back into the radical expression.
(−343)43=13,841,287,2013\sqrt[3]{(-343)^4} = \sqrt[3]{13,841,287,201}

STEP 6

Calculate the cube root of13,841,287,201.
13,841,287,2013=2401\sqrt[3]{13,841,287,201} =2401So, (−343)43=2401(-343)^{\frac{4}{3}} =2401.

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