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Simplify the expression:
[tex]\[ (18)^{\frac{1}{3}} \times (768)^{\frac{1}{3}} \][/tex]


Sagot :

Certainly! Let's break down the expression step-by-step:

We have the expression [tex]\((18)^{\frac{1}{3}} \times (768)^{\frac{1}{3}}\)[/tex].

### Step 1: Evaluate [tex]\((18)^{\frac{1}{3}}\)[/tex]

The exponent [tex]\(\frac{1}{3}\)[/tex] represents the cube root. So, we need to find the cube root of 18. The cube root of 18 is approximately:

[tex]\[ (18)^{\frac{1}{3}} \approx 2.6207413942088964 \][/tex]

### Step 2: Evaluate [tex]\((768)^{\frac{1}{3}}\)[/tex]

Similarly, we need to find the cube root of 768. The cube root of 768 is approximately:

[tex]\[ (768)^{\frac{1}{3}} \approx 9.157713940426653 \][/tex]

### Step 3: Multiply the results

Now, we multiply the two results from the previous steps:

[tex]\[ 2.6207413942088964 \times 9.157713940426653 \approx 23.999999999999993 \][/tex]

### Final Answer

So, the result of the expression [tex]\((18)^{\frac{1}{3}} \times (768)^{\frac{1}{3}}\)[/tex] is approximately:

[tex]\[ 23.999999999999993 \][/tex]

There you have a step-by-step solution for the given expression!