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

Answer 1

Hazel Anglin

#2/3#

If you consider the numerator firstly

#2x^(-3)xxx^5#

when multiplying terms with powers we effectively add the powers

#=># #2x^2#

Now we have #(2x^2)/(3x^2)# #=># #2/3#

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Answer 2

Savannah Anderson

see below

We have, #frac{2xx x ^-3xxx^5}(3x^2)# Simplifying,we get, #frac{2}3 xxx^(5-3-2)

Or, #frac{2}3xx x^0# which comes out to be #2//3#

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Answer 3

Isaiah Anthony

To simplify the expression ( \frac{{2x^{-3} \cdot x^5}}{{3x^2}} ), apply the laws of exponents:

Combine the like terms in the numerator and denominator.
Apply the properties of exponents to simplify the expression.

( \frac{{2x^{-3} \cdot x^5}}{{3x^2}} )

First, simplify the numerator:

( 2x^{-3} \cdot x^5 = 2x^{5-3} = 2x^2 )

Now, rewrite the expression:

( \frac{{2x^2}}{{3x^2}} )

Now, divide the coefficients and subtract the exponents:

( \frac{2}{3}x^{2-2} )

( \frac{2}{3}x^0 )

Any non-zero number raised to the power of zero is equal to 1, so ( x^0 = 1 ).

( \frac{2}{3} \times 1 = \frac{2}{3} )

So, the simplified expression is ( \frac{2}{3} ).

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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.