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How do you simplify #((m^2)^2z^3zd)/(mz^5d^3)#?

Answer 1

Eva Adamson

#(m^3)/(zd^2)#

Simplify #((m^2)^2z^3zd)/(mz^5d^3)#.

First apply power rule #(b^m)^n=b^(m*n)#.

#(m^((2*2))z^3zd)/(mz^5d^3)#

#(m^4z^3zd)/(mz^5d^3)#

Apply product rule #a^ma^n=a^((m+n)).# (Reminder: #b=b^1#).

#(m^4z^3z^1d)/(mz^5d^3)#

#(m^4z^((3+1))d)/(mz^5d^3)#

Simplify.

#(m^4z^4d)/(mz^5d^3)#

Apply quotient rule #a^m/a^n=a^((m-n))#.

#m^((4-1))z^((4-5))d^((1-3))#

Simplify.

#m^3z^(-1)d^(-2)#

Apply negative exponent rule #a^(-m)=1/a^m#.

#(m^3)/(zd^2)#

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Answer 2

Abigail Allen

To simplify the expression ((m^2)^2z^3zd)/(mz^5d^3), you can use the properties of exponents and cancel out common factors. Simplifying step by step:

((m^2)^2z^3zd)/(mz^5d^3)
((m^4)z^3zd)/(mz^5d^3)
(m^4z^4)/(z^5d^2)
(m^4z^(4-5))/(d^2)
(m^4z^(-1))/(d^2)
m^4z^(-1)d^(-2)

Therefore, the simplified expression is m^4z^(-1)d^(-2).

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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.