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How do you simplify #(x^4)^2/(x^3)^5#?

Answer 1

Hazel Anglin

#x ^-7#

#(x ^4) ^2# / #(x ^3) ^5#

#(x ^4.2#) / #(x ^3.5)#

#(x ^8#) / #(x ^15)#

applying law of exponents of division we get;

#x ^-7#

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Answer 2

Savannah Anderson

To simplify ((x^4)^2/(x^3)^5), first apply the exponent rule for powers raised to another power, which states that ((a^m)^n = a^{m \times n}).

So, ((x^4)^2 = x^{4 \times 2} = x^8) and ((x^3)^5 = x^{3 \times 5} = x^{15}).

Then, divide (x^8) by (x^{15}) by subtracting the exponents when dividing like bases, which gives:

[\frac{x^8}{x^{15}} = x^{8-15} = x^{-7}].

Therefore, ((x^4)^2/(x^3)^5) simplifies to (x^{-7}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.