## Which shows the following expression after the negative exponents have been eliminated? m^7 n^3/ mn^-1 assume m=0 and n=0

Question

Which shows the following expression after the negative exponents have been eliminated? m^7 n^3/ mn^-1 assume m=0 and n=0

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1. Given expression is [tex] frac{m^7n^3}{mn^{-1}} [/tex].

where [tex] m neq 0, n neq 0, [/tex]

Now we have to simplify this and find the next step so that negative exponent gets eliminated.

We know that when negative exponent changes sign, then it moves from numerator to denominator or from denominator to numerator as shown in the formula:

[tex] x^{-m}=frac{1}{x^m} [/tex]

or[tex] frac{1}{x^{-m}}=x^{m} [/tex]

n has negative exponent in denominator so it will move to numerator and we get:

[tex] frac{m^7n^3n^1}{m} [/tex]

or [tex] frac{m^7n^3n}{m} [/tex]

Hence final answer is [tex] frac{m^7n^3n}{m} [/tex].

[tex]frac{m^7n^3n^1}{m}=m^6n^4[/tex]

Step-by-step explanation:

A negative exponent tells us to switch sides of the fraction. Since the only variable with a negative exponent is n^(-1), we move it to the top of the fraction and the exponent becomes positive. This gives us

[tex]frac{m^7n^3n^1}{m}[/tex]

We can go on to combine the exponents of n using the product property of exponents (if two powers with the same base are multiplied, we can add their exponents):

[tex]frac{m^7n^4}{m}[/tex]

Since we have an m on the top and the bottom of the fraction, we can subtract their exponents using the product division property:

[tex]m^6n^4[/tex]