solve this, don't bother using Chatbots, as they will say it's 1/125 but my teacher says it wrong, so solve it yourself, challenge yourself, this is for the people who actually studies
[tex] {25}^{ - \frac{3}{2} } [/tex]
[tex] {25}^{ - \frac{3}{2} } [/tex]
Answers & Comments
Answer:
To solve the expression {25}^{-\frac{3}{2}}, we can rewrite it using the exponent rule that states {a}^{-b} = \frac{1}{a^b}.
So, {25}^{-\frac{3}{2}} = \frac{1}{25^{\frac{3}{2}}}.
Now, let's simplify the expression 25^{\frac{3}{2}}.
We know that {\left(a^b\right)}^c = a^{b \cdot c}.
Therefore, 25^{\frac{3}{2}} = {\left(25^{\frac{1}{2}}\right)}^3.
The square root of 25 is 5, so 25^{\frac{1}{2}} = 5.
Substituting this value back into the expression, we have 5^3.
5^3 = 5 \cdot 5 \cdot 5 = 125.
Now, let's substitute the simplified value back into the original expression:
\frac{1}{25^{\frac{3}{2}}} = \frac{1}{125}.
Therefore, the value of {25}^{-\frac{3}{2}} is \frac{1}{125}.
:D