To solve the equation \( x^{5/4} = 243 \), we will first rewrite the equation in terms of \( x \).
-
Isolate \( x \):
We want to get \( x \) by itself, so we can raise both sides to the reciprocal of \( 5/4 \), which is \( 4/5 \):\[ x = 243^{4/5} \]
-
Calculate \( 243^{4/5} \):
First, we find \( 243 \) as a power of a smaller number. Notably, \( 243 = 3^5 \).Therefore, we can rewrite the expression:
\[ 243^{4/5} = (3^5)^{4/5} \]
Using the property of exponents \((a^m)^n = a^{m \cdot n}\):
\[ (3^5)^{4/5} = 3^{(5 \cdot 4/5)} = 3^4 \]
-
Calculate \( 3^4 \):
Calculating \( 3^4 \):\[ 3^4 = 81 \]
Thus, the solution to the equation \( x^{5/4} = 243 \) is:
\[ x = 81 \]
Therefore, 81 is the correct answer because it is derived from solving the equation correctly.
2 answers