Answer :
To solve the given expression [tex]\(\left(\frac{-t}{3}\right)^3\)[/tex], we will break it down step-by-step.
1. Identify the base and the exponent:
The base of the expression is [tex]\(\frac{-t}{3}\)[/tex] and the exponent is 3.
2. Apply the exponent to both the numerator and the denominator of the fraction:
When raising a fraction to a power, raise both the numerator and the denominator to that power:
[tex]\[ \left(\frac{-t}{3}\right)^3 = \frac{(-t)^3}{3^3} \][/tex]
3. Calculate the numerator raised to the power:
The expression for the numerator is [tex]\((-t)^3\)[/tex]. Raise [tex]\(-t\)[/tex] to the power of 3:
[tex]\[ (-t)^3 = -t^3 \][/tex]
4. Calculate the denominator raised to the power:
The expression for the denominator is [tex]\(3^3\)[/tex]. Raise 3 to the power of 3:
[tex]\[ 3^3 = 27 \][/tex]
5. Combine the results of the numerator and the denominator:
Substitute the results back into the fraction:
[tex]\[ \frac{(-t)^3}{3^3} = \frac{-t^3}{27} \][/tex]
Thus, the simplified form of the expression [tex]\(\left(\frac{-t}{3}\right)^3\)[/tex] is:
[tex]\[ \boxed{-\frac{t^3}{27}} \][/tex]
1. Identify the base and the exponent:
The base of the expression is [tex]\(\frac{-t}{3}\)[/tex] and the exponent is 3.
2. Apply the exponent to both the numerator and the denominator of the fraction:
When raising a fraction to a power, raise both the numerator and the denominator to that power:
[tex]\[ \left(\frac{-t}{3}\right)^3 = \frac{(-t)^3}{3^3} \][/tex]
3. Calculate the numerator raised to the power:
The expression for the numerator is [tex]\((-t)^3\)[/tex]. Raise [tex]\(-t\)[/tex] to the power of 3:
[tex]\[ (-t)^3 = -t^3 \][/tex]
4. Calculate the denominator raised to the power:
The expression for the denominator is [tex]\(3^3\)[/tex]. Raise 3 to the power of 3:
[tex]\[ 3^3 = 27 \][/tex]
5. Combine the results of the numerator and the denominator:
Substitute the results back into the fraction:
[tex]\[ \frac{(-t)^3}{3^3} = \frac{-t^3}{27} \][/tex]
Thus, the simplified form of the expression [tex]\(\left(\frac{-t}{3}\right)^3\)[/tex] is:
[tex]\[ \boxed{-\frac{t^3}{27}} \][/tex]
Answer:
[tex]\displaystyle \frac{-t^3}{27}[/tex]
Step-by-step explanation:
We will simplify the given expression. Remember that when raising a fraction to a power, you raise both the numerator and denominator separately.
Given:
[tex]\displaystyle (\frac{-t}{3} )^3[/tex]
Raise the fraction to a power:
[tex]\displaystyle \frac{(-t)^3}{(3)^3}[/tex]
Cube both the numerator and the denominator:
➜ -t * -t * -t = -t
➜ 3 * 3 * 3 = 27
[tex]\displaystyle \frac{-t^3}{27}[/tex]
This gives us our final answer. Please note that the negative sign can be placed in the numerator, denominator, or in front of the fraction.
[tex]\displaystyle \boxed{-\frac{t^3}{27}}[/tex]
