Simplifying the Exponential Expression $(25)^{\frac{3}{2}}$
To simplify the expression $(25)^{\frac{3}{2}}$, we can use the properties of exponents.
Exponent Rule Application
Recall the exponent rule: $(a^m)^n = a^{m \times n}$. We can rewrite 25 as $5^2$. Substituting this into the expression gives:
$ (25)^{\frac{3}{2}} = (5^2)^{\frac{3}{2}} $Now, apply the rule $(a^m)^n = a^{m \times n}$:
$ (5^2)^{\frac{3}{2}} = 5^{(2 \times \frac{3}{2})} = 5^3 $Calculating the Final Value
Finally, calculate $5^3$:
$ 5^3 = 5 \times 5 \times 5 = 125 $Therefore, the simplified value of $(25)^{\frac{3}{2}}$ is 125.
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