Simplify: (4d^(3))(-6d^(5)) Answer:

Identify Coefficients and Like Terms: Identify the coefficients and the like terms. The coefficients are the numerical parts of the terms, which are 4 and -6. The like terms are the d terms with exponents, d^(3) and d^(5).Multiply Coefficients: Multiply the coefficients. Multiply 4 by -6 to get the new coefficient. 4 * -6 = -24Apply Product Rule for Exponents: Apply the product rule for exponents. The product rule states that when multiplying like bases, you add the exponents. So, add the exponents 3 and 5. 3 + 5 = 8Combine Results: Combine the results from Step 2 and Step 3. Combine the new coefficient from Step 2 with the result of the exponent addition from Step 3 to get the final answer. -24d^(8)

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Simplify: $\newline$ $\left(4 d^{3}\right)\left(-6 d^{5}\right)$ $\newline$ Answer:

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Algebra 2

Multiplication with rational exponents

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Q. Simplify:

\newline

\left(4 d^{3}\right)\left(-6 d^{5}\right)

\newline

Answer:

Identify Coefficients and Like Terms: Identify the coefficients and the like terms. The coefficients are the numerical parts of the terms, which are $4$ and $-6$ . The like terms are the $d$ terms with exponents, $d^{3}$ and $d^{5}$ .
Multiply Coefficients: Multiply the coefficients. $\newline$ Multiply $4$ by $-6$ to get the new coefficient. $\newline$ $4 \times -6 = -24$
Apply Product Rule for Exponents: Apply the product rule for exponents. The product rule states that when multiplying like bases, you add the exponents. So, add the exponents $3$ and $5$ . $3 + 5 = 8$
Combine Results: Combine the results from Step $2$ and Step $3$ . Combine the new coefficient from Step $2$ with the result of the exponent addition from Step $3$ to get the final answer. $-24d^{8}$