Write the following as an exponential expression. root(4)(13^(3))

Apply Exponent Property: We have the expression root(4)(13^(3)). According to the property of exponents, (a^(m))^(n) = a^(m*n), we can multiply the exponents together when raising a power to another power. So, we will multiply the exponent 3 of 13 by 1/4 to convert the fourth root into an exponential expression.Multiply Exponents: Performing the multiplication of the exponents, we get 13^(3*(1/4)) which simplifies to 13^(3/4). This is the exponential expression equivalent to the fourth root of 13 cubed.Simplify Exponential Expression: Now, we check for any mathematical errors. The steps followed the exponent rules correctly, and the multiplication of the exponents was done accurately.

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Q. Write the following as an exponential expression.

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\sqrt[4]{13^{3}}

Apply Exponent Property: We have the expression $\sqrt[4]{13^{3}}$ . According to the property of exponents, $(a^{m})^{n} = a^{m*n}$ , we can multiply the exponents together when raising a power to another power. $\newline$ So, we will multiply the exponent $3$ of $13$ by $\frac{1}{4}$ to convert the fourth root into an exponential expression.
Multiply Exponents: Performing the multiplication of the exponents, we get $13^{3\times(1/4)}$ which simplifies to $13^{3/4}$ . This is the exponential expression equivalent to the fourth root of $13$ cubed.
Simplify Exponential Expression: Now, we check for any mathematical errors. The steps followed the exponent rules correctly, and the multiplication of the exponents was done accurately.