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Write in exponential notation:

((5^(2))^(3))^(2)

Write in exponential notation: $\newline$ $\left(\left(5^{2}\right)^{3}\right)^{2}$

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Power property of logarithms

Full solution

Q. Write in exponential notation:

\newline

\left(\left(5^{2}\right)^{3}\right)^{2}

Apply Power Rule: Apply the power of a power rule to the expression. $\newline$ The power of a power rule states that $(a^{m})^{n} = a^{m*n}$ . We will apply this rule to the given expression $((5^{2})^{3})^{2}$ . $\newline$ Calculation: $((5^{2*3})^{2})$
Multiply Exponents: Multiply the exponents inside the parentheses. $\newline$ We will multiply the exponents $2$ and $3$ inside the parentheses. $\newline$ Calculation: $(5^{6})^{2}$
Apply Power Rule: Apply the power of a power rule again to the expression. $\newline$ Now we will apply the power of a power rule again to the expression $(5^{6})^{2}$ . $\newline$ Calculation: $5^{6*2}$
Multiply Exponents: Multiply the exponents outside the parentheses. $\newline$ We will multiply the exponents $6$ and $2$ outside the parentheses. $\newline$ Calculation: $5^{12}$

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