Answer :
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.
