products of irrational square roots practice

Question

what is 3^√54 simplified

Answer 1

To simplify \( 3^{\sqrt{54}} \), we can start by simplifying the square root term.

First, let's simplify \( \sqrt{54} \): \[ \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6} \]

Now we can substitute this back into the expression: \[ 3^{\sqrt{54}} = 3^{3\sqrt{6}} \]

Next, we can rewrite this using the properties of exponents: \[ 3^{3\sqrt{6}} = (3^3)^{\sqrt{6}} = 27^{\sqrt{6}} \]

Thus, the simplified form of \( 3^{\sqrt{54}} \) is: \[ 27^{\sqrt{6}} \]