# How do you simplify #(3r^7)/(2r^2)^4#?

This fraction is simplified by using the power identities of powers with same base

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To simplify (3r^7)/(2r^2)^4, first simplify the expression inside the parentheses: (2r^2)^4 = 2^4 * (r^2)^4 = 16 * r^(2*4) = 16r^8. Then, divide 3r^7 by 16r^8. Since the bases are the same, divide the coefficients and subtract the exponents: 3/16 * r^(7-8) = 3/16 * r^(-1). Simplify the expression by moving the variable with a negative exponent to the denominator: 3/(16r).

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