Express the following fraction in simplest form, only using positive exponents. (2(p^(-3)b^(5))^(-2))/(3b^(-2)) Answer:

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Express the following fraction in simplest form, only using positive exponents.  (2(p^(-3)b^(5))^(-2))/(3b^(-2)) Answer:

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Write Expression, Identify Exponents: Write down the given expression and identify the negative exponents. The given expression is (2(p^(-3)b^(5))^(-2))/(3b^(-2)). We need to simplify this expression and express it with only positive exponents.Apply Negative Exponent Rule: Apply the negative exponent rule, which states that a^(-n) = 1/(a^n), to the terms with negative exponents. (2(p^(-3)b^(5))^(-2))/(3b^(-2)) becomes (2/(p^(3)b^(-5))^2)/(3/b^(2)).Apply Power Rule: Simplify the expression by applying the power rule, which states that (a^m)^n = a^(m*n). (2/(p^(3)b^(-5))^2)/(3/b^(2)) becomes (2/(p^(6)b^(-10)))/(3/b^(2)).Eliminate Negative Exponents: Multiply the numerator and the denominator by b^(10) to eliminate the negative exponent in the denominator. (2b^(10))/(p^(6)b^(-10)) * (b^(10))/(3b^(2)) becomes (2b^(10))/(p^(6)) * (b^(10))/(3b^(2)).Cancel Common Terms: Simplify the expression by canceling out the common b terms and multiplying the numerators and denominators. (2b^(10))/(p^(6)) * (b^(10))/(3b^(2)) becomes (2b^(20))/(3p^(6)b^(2)).Combine B Terms: Simplify the expression by combining the b terms. (2b^(20))/(3p^(6)b^(2)) becomes (2b^(18))/(3p^(6)).Check for Common Factors: Check for any common factors between the numerator and the denominator that can be simplified. There are no common factors between 2b^(18) and 3p^(6), so the expression is already in its simplest form.

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{2\left(p^{-3} b^{5}\right)^{-2}}{3 b^{-2}}$ $\newline$ Answer:

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Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{2\left(p^{-3} b^{5}\right)^{-2}}{3 b^{-2}}$ $\newline$ Answer: