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[(5^(3))^(4)]_(=)^(2)

$\left[\left(5^{3}\right)^{4}\right]_{=}^{2}$

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Evaluate rational exponents

Full solution

Q.

\left[\left(5^{3}\right)^{4}\right]_{=}^{2}

Identify Base and Exponents: Identify the base and the exponents in the expression $[(5^{(3)})^{(4)}]^{(2)}$ . $\newline$ Base: $5$ $\newline$ Exponents: $3$ , $4$ , and $2$
Use Power of Power Rule: Use the power of a power rule $(a^{m})^{n} = a^{m*n}$ to simplify the expression. $[(5^{3})^{4}]^{2} = 5^{3*4*2}$
Calculate Exponent Product: Calculate the product of the exponents. $3\times4\times2 = 12\times2 = 24$
Apply Exponent to Base: Apply the calculated exponent to the base. $5^{24}$
Check for Further Simplification: Check if the expression can be simplified further. $5^{24}$ is already in its simplest form.

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