Question

please answer this question and explain step by step
I will make you brainlist​

Answer 1

Answer:

∛ (-a⁶÷ a¹²) × b³ × (c²¹÷ c⁹)

Here I have collected all similar variables on the same side. Let us recall the basic laws of powers.

We know that xᵃ/ xᵇ= xᵃ⁻ᵇ and xᵃ × xᵇ= xᵃ⁺ᵇ.

Applying the first rule to our 'a' variable and 'c' variable we get-

-a⁶⁻¹² = -a⁻⁶

c²¹⁻⁹ = c¹²

Therefore, a simplified form of the given question is ∛⁻a⁶× b³× c¹².

Let us now recall one more law of exponents. √x= $x^{1/2}$ and ∛x = $x^{1/3}$.

So ∛⁻a⁶× b³× c¹² = $-a^{6*1/3}$ × $b^{3*1/3}$ × $c^{12*1/3}$

Therefore, we have the most simplified form of ∛ (-a⁶÷ a¹²) × b³ × (c²¹÷ c⁹) as -a⁻² b¹ c⁴ = -bc⁴/ a².

This is option (d).