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

Question

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

Bytelearn · Accepted Answer

Identify Negative Exponent: Write down the given expression and identify the negative exponent. The given expression is (-5y^(6))/((-3y^(-4))^(4)). We need to simplify this expression and ensure that all exponents are positive.Apply Power Rule: Apply the power rule to the denominator. When an exponent is raised to another exponent, we multiply the exponents. In this case, we have (-3y^(-4))^4. We will apply the power rule to the y term. (-3y^(-4))^4 = (-3)^4 * (y^(-4))^4 = 81 * y^(-16)Rewrite Negative Exponent: Rewrite the negative exponent as a positive exponent. To convert a negative exponent to a positive exponent, we take the reciprocal of the base. So, y^(-16) becomes 1/y^(16). 81 * y^(-16) = 81/y^(16)Combine Numerator and Denominator: Combine the numerator and the simplified denominator. Now we have the original numerator (-5y^(6)) and the simplified denominator (81/y^(16)). We will combine these to form a single fraction. (-5y^(6)) / (81/y^(16)) = (-5y^(6)) * (y^(16)/81)Multiply Terms with Same Base: Multiply the terms with the same base using the property of exponents. When multiplying terms with the same base, we add the exponents. In this case, we have y^(6) * y^(16). (-5y^(6)) * (y^(16)/81) = (-5 * y^(6+16)) / 81 = (-5 * y^(22)) / 81Simplify Fraction: Simplify the fraction if possible. In this case, there are no common factors between the numerator and the denominator, so the fraction is already in its simplest form. (-5 * y^(22)) / 81

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

Full solution

More problems from Multiplication with rational exponents

Related topics

Express the following fraction in simplest form, only using positive exponents.\newline−5y6(−3y−4)4 \frac{-5 y^{6}}{\left(-3 y^{-4}\right)^{4}} (−3y−4)4−5y6​\newlineAnswer:

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