Question

Which expression is equivalent to the given expression? (10c⁶ d⁻5) (2c⁻5 d⁴)

a. (20c)
b. (20c⁶d⁻¹)
c. (20c⁶d⁻¹)
d. (20c⁶d¹)

Answer 1

The expression (10c⁶ d⁻⁵) (2c⁻⁵ d⁴) is equivalent to (20c⁶ d⁻¹). Therefore, the correct equivalent expression is (20c⁶d⁻¹) (option b).

Step-by-step explanation:

The expression (10c⁶ d⁻⁵) (2c⁻⁵ d⁴) can be simplified using the rules of exponents.

When multiplying exponential expressions with the same base, you add the exponents.

In this case, the 'c' terms have exponents of 6 and -5, and the 'd' terms have exponents of -5 and 4.

So, the simplified expression is:

(10c⁶ d⁻⁵) (2c⁻⁵ d⁴) = (10 * 2) c⁶⁺⁻⁵ d⁻⁵⁺⁴ = 20c d⁻¹ = (20c⁶d⁻¹)

Therefore, the correct equivalent expression is (20c⁶d⁻¹) (option b).