IDNLearn.com provides a user-friendly platform for finding and sharing accurate answers. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.
Sagot :
Sure! Let's solve the expression [tex]\(\left(\frac{8}{21}\right)^{\frac{2}{3}}\)[/tex].
### Step 1: Simplify the base
First, we will simplify the fraction [tex]\(\frac{8}{21}\)[/tex] into a decimal form to make calculations easier:
[tex]\[ \frac{8}{21} \approx 0.38095238095238093 \][/tex]
### Step 2: Simplify the exponent
Next, we simplify the exponent [tex]\(\frac{2}{3}\)[/tex] into a decimal form:
[tex]\[ \frac{2}{3} \approx 0.6666666666666666 \][/tex]
### Step 3: Calculate the power
Now, we need to raise the base [tex]\(0.38095238095238093\)[/tex] to the power of [tex]\(0.6666666666666666\)[/tex].
[tex]\[ 0.38095238095238093^{0.6666666666666666} \approx 0.5255093669297373 \][/tex]
### Step 4: Write the final answer
So, the expression [tex]\(\left(\frac{8}{21}\right)^{\frac{2}{3}}\)[/tex] simplifies to approximately:
[tex]\[ 0.5255093669297373 \][/tex]
In summary, the steps involve converting the fraction and exponent to their decimal form, computing the power, and then writing the result.
### Step 1: Simplify the base
First, we will simplify the fraction [tex]\(\frac{8}{21}\)[/tex] into a decimal form to make calculations easier:
[tex]\[ \frac{8}{21} \approx 0.38095238095238093 \][/tex]
### Step 2: Simplify the exponent
Next, we simplify the exponent [tex]\(\frac{2}{3}\)[/tex] into a decimal form:
[tex]\[ \frac{2}{3} \approx 0.6666666666666666 \][/tex]
### Step 3: Calculate the power
Now, we need to raise the base [tex]\(0.38095238095238093\)[/tex] to the power of [tex]\(0.6666666666666666\)[/tex].
[tex]\[ 0.38095238095238093^{0.6666666666666666} \approx 0.5255093669297373 \][/tex]
### Step 4: Write the final answer
So, the expression [tex]\(\left(\frac{8}{21}\right)^{\frac{2}{3}}\)[/tex] simplifies to approximately:
[tex]\[ 0.5255093669297373 \][/tex]
In summary, the steps involve converting the fraction and exponent to their decimal form, computing the power, and then writing the result.
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.