Simplify (8^(4))/((4^(8)))

Identify and Rewrite Expression: Identify the given expression and rewrite it to make it easier to work with. The expression is (8^(4))/((4^(8))/(8x)). We can simplify this by multiplying by the reciprocal of the denominator. (8^(4)) * ((8x)/(4^(8))).Simplify Bases of Exponents: Simplify the bases of the exponents where possible. 8 is 2^3, and 4 is 2^2. Rewrite the expression with these bases to get: (2^(3*4)) * ((8x)/(2^(2*8))).Simplify Exponents: Simplify the exponents. (2^(12)) * ((8x)/(2^(16))).Divide Exponents: Divide the exponents with the same base by subtracting the exponents. (2^(12-16)) * (8x).Calculate New Exponent: Calculate the new exponent. (2^(-4)) * (8x).Further Simplify Expression: Simplify the expression further. Since 2^(-4) is 1/(2^4), we can rewrite the expression as: (1/(2^4)) * (8x).Calculate and Simplify: Calculate 2^4 and simplify the expression. 2^4 is 16, so we have: (1/16) * (8x).Multiply Terms: Multiply the terms. (8x)/16.Simplify Fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 8. (x/2).

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Q. Simplify

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

Identify and Rewrite Expression: Identify the given expression and rewrite it to make it easier to work with. $\newline$ The expression is $(8^{4})/((4^{8})/(8x))$ . $\newline$ We can simplify this by multiplying by the reciprocal of the denominator. $\newline$ $(8^{4}) \times ((8x)/(4^{8}))$ .
Simplify Bases of Exponents: Simplify the bases of the exponents where possible. $8$ is $2^3$ , and $4$ is $2^2$ . Rewrite the expression with these bases to get: $(2^{3*4}) * ((8x)/(2^{2*8}))$ .
Simplify Exponents: Simplify the exponents. $(2^{12}) \times \left(\frac{8x}{2^{16}}\right)$ .
Divide Exponents: Divide the exponents with the same base by subtracting the exponents. \(2^{ $12$ $-16$ }) \times ( $8$ x)\
Calculate New Exponent: Calculate the new exponent. $\newline$ $(2^{-4}) \times (8x)$ .
Further Simplify Expression: Simplify the expression further. $\newline$ Since $2^{-4}$ is $1/(2^4)$ , we can rewrite the expression as: $\newline$ $(1/(2^4)) \cdot (8x)$ .
Calculate and Simplify: Calculate $2^4$ and simplify the expression. $\newline$ $2^4$ is $16$ , so we have: $\newline$ $(1/16) \cdot (8x)$ .
Multiply Terms: Multiply the terms. $\newline$ $(\frac{8x}{16})$ .
Simplify Fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $8$ . $\frac{x}{2}$ .