Express the following fraction in simplest form, only using positive exponents. ((4x^(-5)k^(3))^(-5))/(12x^(-6)k^(-8)) Answer:

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Express the following fraction in simplest form, only using positive exponents.  ((4x^(-5)k^(3))^(-5))/(12x^(-6)k^(-8)) Answer:

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Write Expression, Identify Exponents: Write down the given expression and identify the negative exponents. The given expression is ((4x^(-5)k^(3))^(-5))/(12x^(-6)k^(-8)). We need to simplify this expression and express it with only positive exponents.Apply Negative Exponent Rule: Apply the negative exponent rule to the numerator. The negative exponent rule states that a^(-n) = 1/(a^n). We will apply this rule to the entire numerator. ((4x^(-5)k^(3))^(-5)) becomes (1/(4x^(-5)k^(3))^5).Simplify Denominator: Simplify the denominator by applying the negative exponent rule. The negative exponent rule will also be applied to each term in the denominator. 12x^(-6)k^(-8) becomes 12/(x^6k^8).Combine Numerator and Denominator: Combine the numerator and denominator. Now we have (1/(4x^(-5)k^(3))^5) / (12/(x^6k^8)). This can be rewritten as (1/(4^5x^(-25)k^(15))) * (x^6k^8/12).Multiply Terms: Simplify the expression by multiplying the terms. We multiply the numerators and the denominators separately. This gives us (x^6k^8)/(4^5x^(-25)k^(15) * 12).Simplify Powers and Combine: Simplify the powers of 4 and combine like terms. 4^5 is 1024. We also add the exponents of like bases. This results in (x^(6-(-25))k^(8-15))/(1024 * 12).Perform Exponent Arithmetic: Perform the exponent arithmetic and simplify the fraction. Adding the exponents of x and subtracting the exponents of k gives us x^(31)k^(-7). Simplify 1024 * 12 to get 12288. The expression is now x^(31)k^(-7)/12288.Apply Negative Exponent Rule: Apply the negative exponent rule to k^(-7) to make the exponent positive. k^(-7) becomes 1/k^7. The final expression is x^(31)/(12288k^7).

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{\left(4 x^{-5} k^{3}\right)^{-5}}{12 x^{-6} k^{-8}}$ $\newline$ Answer:

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Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{\left(4 x^{-5} k^{3}\right)^{-5}}{12 x^{-6} k^{-8}}$ $\newline$ Answer: