Identify Base and Exponent: Identify the base and the exponent in 8^(4) and the divisor 4. In 8^(4)/4, Base: 8 Exponent: 4 Divisor: 4Express 8 as Term: Express 8 as a term raised to the power of 3. 8 = 2*2*2 = 2^3Express Using Base 2: Express 8^(4) using the base 2. (8^(4))/(4) = ((2^3)^(4))/4 = (2^(3*4))/4 = (2^(12))/4Simplify by Dividing: Simplify the expression by dividing 2^(12) by 4. Since 4 is 2^2, we can write the division as a subtraction of exponents. (2^(12))/(2^2) = 2^(12-2) = 2^(10)Write Final Answer: Write the final answer. The simplified result of dividing 8 to the power of 4 by 4 is 2 to the power of 10.

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$\frac{8^{4}}{4}$

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Algebra 2

Evaluate rational exponents

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\frac{8^{4}}{4}

Identify Base and Exponent: Identify the base and the exponent in $8^{4}$ and the divisor $4$ . In $\frac{8^{4}}{4}$ , Base: $8$ Exponent: $4$ Divisor: $4$
Express $8$ as Term: Express $8$ as a term raised to the power of $3$ . $\newline$ $8 = 2 \times 2 \times 2$ $\newline$ $= 2^3$
Express Using Base $2$ : Express $8^{4}$ using the base $2$ . $\newline$ $(8^{4})/(4)$ $\newline$ = $((2^3)^{4})/4$ $\newline$ = $(2^{3*4})/4$ $\newline$ = $(2^{12})/4$
Simplify by Dividing: Simplify the expression by dividing $2^{12}$ by $4$ . Since $4$ is $2^2$ , we can write the division as a subtraction of exponents. $\frac{2^{12}}{2^2}$ = $2^{12-2}$ = $2^{10}$
Write Final Answer: Write the final answer. $\newline$ The simplified result of dividing $8$ to the power of $4$ by $4$ is $2$ to the power of $10$ .