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9^((3)/(4))=

$9^{\frac{3}{4}}$ =

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Evaluate integers raised to positive rational exponents

Full solution

Q.

9^{\frac{3}{4}}

=

Identify base and exponent: Identify the base and the exponent. $\newline$ In $9^{3/4}$ , the base is $9$ and the exponent is $3/4$ .
Express $9$ as power of $4$ : Express $9$ as a term raised to the power of $4$ . Since $9$ is a perfect square, we can write it as $3^2$ . However, we need to express it as a power of $4$ for this problem. To do this, we can write $9$ as $(3^2)$ and then raise it to the power of $(1/2)$ to get the fourth root. $9 = (3^2)^{(1/2)} = 3^{2*(1/2)} = 3^1 = 3$ But we need to express it as a power of $4$ , so we need to take the square root of $3$ to get the fourth root of $9$ . $(3^{(1/2)})^2 = 3^{2*(1/2)} = 3^1 = 3$ This is incorrect because we have not expressed $9$ as a power of $4$ . We need to find a way to express $9$ as a power that involves the fourth root.

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