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Sagot :
To find [tex]\(27^{\frac{4}{3}}\)[/tex], we can follow these steps:
1. First, recall that the exponent [tex]\(\frac{4}{3}\)[/tex] can be broken down into two parts: the cube root (i.e., raising to the power of [tex]\(\frac{1}{3}\)[/tex]) and then raising to the power of 4.
2. We know that [tex]\(27\)[/tex] can be expressed as [tex]\(3^3\)[/tex]. Therefore, we can write:
[tex]\[ 27 = 3^3 \][/tex]
3. Applying the exponent [tex]\(\frac{4}{3}\)[/tex] to [tex]\(27\)[/tex]:
[tex]\[ 27^{\frac{4}{3}} = (3^3)^{\frac{4}{3}} \][/tex]
4. Using the property of exponents [tex]\((a^m)^n = a^{m \cdot n}\)[/tex], we can simplify:
[tex]\[ (3^3)^{\frac{4}{3}} = 3^{3 \cdot \frac{4}{3}} = 3^4 \][/tex]
5. Calculate [tex]\(3^4\)[/tex]:
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \][/tex]
Hence, the value of [tex]\(27^{\frac{4}{3}}\)[/tex] is [tex]\(81\)[/tex].
The options given are:
- 12
- 108
- 81
- 4
The correct answer is:
[tex]\[ \boxed{81} \][/tex]
1. First, recall that the exponent [tex]\(\frac{4}{3}\)[/tex] can be broken down into two parts: the cube root (i.e., raising to the power of [tex]\(\frac{1}{3}\)[/tex]) and then raising to the power of 4.
2. We know that [tex]\(27\)[/tex] can be expressed as [tex]\(3^3\)[/tex]. Therefore, we can write:
[tex]\[ 27 = 3^3 \][/tex]
3. Applying the exponent [tex]\(\frac{4}{3}\)[/tex] to [tex]\(27\)[/tex]:
[tex]\[ 27^{\frac{4}{3}} = (3^3)^{\frac{4}{3}} \][/tex]
4. Using the property of exponents [tex]\((a^m)^n = a^{m \cdot n}\)[/tex], we can simplify:
[tex]\[ (3^3)^{\frac{4}{3}} = 3^{3 \cdot \frac{4}{3}} = 3^4 \][/tex]
5. Calculate [tex]\(3^4\)[/tex]:
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \][/tex]
Hence, the value of [tex]\(27^{\frac{4}{3}}\)[/tex] is [tex]\(81\)[/tex].
The options given are:
- 12
- 108
- 81
- 4
The correct answer is:
[tex]\[ \boxed{81} \][/tex]
Answer:
81
Step-by-step explanation:
[tex]27^{\frac{4}{3} }[/tex] can also be written as [tex]\sqrt[3]{27^{4} }[/tex]
You can now solve for the answer using this rewritten equation *remember to use your calculator!*:
- [tex]\sqrt[3]{27^{4} }[/tex]
- [tex]\sqrt[3]{531441 }[/tex]
- =81
Your answer is 81
Hope this helped!
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