Express the following fraction in simplest form, only using positive exponents. (4(d^(-4)q^(-1))^(2))/(4d^(10)q^(-2)) Answer:

Question

Express the following fraction in simplest form, only using positive exponents.  (4(d^(-4)q^(-1))^(2))/(4d^(10)q^(-2)) Answer:

Bytelearn · Accepted Answer

Write & Identify: Write down the given expression and identify the negative exponents. The given expression is (4(d^(-4)q^(-1))^(2))/(4d^(10)q^(-2)). We need to simplify this expression and express it with only positive exponents.Apply Power Rule: Apply the power to a product rule to the numerator. According to the power to a product rule, (ab)^n = a^n * b^n. So, (4(d^(-4)q^(-1))^(2)) becomes 4^2 * (d^(-4))^2 * (q^(-1))^2.Simplify Numerator: Simplify the numerator using the power of a power rule. According to the power of a power rule, (a^m)^n = a^(m*n). So, 4^2 * (d^(-4))^2 * (q^(-1))^2 becomes 16 * d^(-8) * q^(-2).Rewrite with Pos Exponents: Rewrite the expression with positive exponents. To convert negative exponents to positive, we use the rule a^(-n) = 1/a^n. So, d^(-8) becomes 1/d^8 and q^(-2) becomes 1/q^2. The numerator is now 16/(d^8 * q^2).Simplify Denominator: Simplify the denominator. The denominator is 4d^(10)q^(-2). We already know that q^(-2) is 1/q^2, so the denominator becomes 4d^(10)/q^2.Combine Numerator & Denominator: Combine the numerator and denominator. Now we have (16/(d^8 * q^2)) / (4d^(10)/q^2). We can simplify this by multiplying by the reciprocal of the denominator.Multiply by Reciprocal: Multiply by the reciprocal of the denominator. Multiplying by the reciprocal, we get (16/(d^8 * q^2)) * (q^2/(4d^(10))).Cancel Common Factors: Cancel out common factors. The q^2 terms cancel out, and we can simplify 16/4 to 4. Now we have 4/(d^8 * d^(10)).Combine D Terms: Combine the d terms using the rule a^m/a^n = a^(m-n). So, 4/(d^8 * d^(10)) becomes 4/d^(8+10) which simplifies to 4/d^(18).

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{4\left(d^{-4} q^{-1}\right)^{2}}{4 d^{10} q^{-2}}$ $\newline$ Answer:

Full solution

More problems from Multiplication with rational exponents

Related topics

Express the following fraction in simplest form, only using positive exponents.\newline4(d−4q−1)24d10q−2 \frac{4\left(d^{-4} q^{-1}\right)^{2}}{4 d^{10} q^{-2}} 4d10q−24(d−4q−1)2​\newlineAnswer:

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{4\left(d^{-4} q^{-1}\right)^{2}}{4 d^{10} q^{-2}}$ $\newline$ Answer: