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.
Similar Questions
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Important Questions from Surds and Indices
The value of (0.3) [{(200 - 146)/(3 × 3 × 3)} - 3] is:
The expression \(\frac{{15\left( {\sqrt {10} + \sqrt 5 } \right)}}{{\sqrt {10\;} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}\) is equal to:
Let \(x = \left( {\frac{{√ {1875} }}{{√ {3888} }} \div \frac{{√ {1200} }}{{\sqrt 768}}} \right) \times \frac{{√ {175} }}{{√ {1792} }}\) . Then √x is equal to:
If \(x = \sqrt {-\sqrt 3 + \sqrt {3 + 8\sqrt {7 + 4\sqrt 3}}}\) where x > 0, then the value of x is equal to:
What is the value of \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}−\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}−\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}\) ?
