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Evaluate the expression:5^3.2 = y

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Given the following expression:


\text{ 5}^{3.2^{}}\text{ = y}

To expand the given exponential expression, we first convert 5.2 into an improper fraction.

We get,


3.2\text{ = 3}(20)/(100)\text{ = 3}(1)/(5)
\text{ 3}(1)/(5)\text{ = }\frac{1\text{ + (3 x 5)}}{5}\text{ = }\frac{1\text{ + 15}}{5}
\text{ = }(16)/(5)

Reconstructing the expression, we get:


\text{ 5}^(3.2)\text{ = y }\rightarrow5^{(16)/(5)}=\text{ y}

When the exponent is a fraction, the numerator remains the exponent of the base while the denominator becomes the degree of the root.

We get,


\text{ 5}^{(16)/(5)}\text{ = y }\rightarrow\text{ }\sqrt[5]{5^(16)}\text{ = y}
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User Ji Cha
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