Question

select the correct answer.
which expression is equivalent to the given expression?
$(10c^{6}d^{-5})(2c^{-5}d^{4})$
a. $\frac{20c}{d}$
b. $20cd$
c. $\frac{20}{c^{30}d^{20}}$
d. $20c^{30}d^{20}$

Explanation:

Step1: Multiply constant terms

$10 \times 2 = 20$

Step2: Combine $c$-terms (add exponents)

$c^{6} \times c^{-5} = c^{6 + (-5)} = c^{1} = c$

Step3: Combine $d$-terms (add exponents)

$d^{-5} \times d^{4} = d^{-5 + 4} = d^{-1} = \frac{1}{d}$

Step4: Multiply all results

$20 \times c \times \frac{1}{d} = \frac{20c}{d}$

Answer:

A. $\frac{20c}{d}$