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Which shows the following expression using positive exponents?
-3a^-2b^3/15a^-7b^-1 a ≠ 0, b ≠ 0

A a^7b^3b^1/15(3)a^2
B -3a^7b^3b^1/15a^2
C -3(-a^2)b^3/15(-a^7)(-b^1)
D 15a^7b^3b^1/-3a^2

Which shows the following expression using positive exponents?
a^3b^-2/ab^-4, a ≠ 0, b ≠ 0
A a^3b^-4/ab^-2
B ab^4/a^3b^2
C -a^3b^4/ab^2
D a^3b^4/ab^2

Which expression is equivalent to (4mn/m^-2n^6)^-2 ? Assume m ≠ 0, n ≠ 0
A n^6/16m^8
B n^10/16m^6
C n^10/8m^8
D 4m^3/n^8

Respuesta :

1) B. -3a^7b^4/15a^2

2)D. a-^3b^4/ab^2
3) B n^12/16m^2n^2m^4. 2 n's cancel on the top and bottom

The given expressions can be converted into the form of positive exponents by using arithmetic operations. For better understanding refer the below solution.

Given :

1st expression - [tex]\dfrac{-3a^{-2}b^3}{15a^{-7}b^{-1}}[/tex]

2nd expression - [tex]\dfrac{a^{3}b^{-2}}{ab^{-4}}[/tex]

3rd expression -  [tex]\left[\dfrac{4mn}{m^{-2}n^{6}}\right ]^{-2}[/tex]

1).

Following steps can be use to determine the 1st expression in positive exponents:

Step 1 - Multiply numerator and denominator by [tex]a^7[/tex].

[tex]=\dfrac{-3a^{-2}b^3}{15a^{-7}b^{-1}}\times \dfrac{a^7}{a^7}[/tex]

[tex]=\dfrac{-3a^{-2}b^3a^7}{15b^{-1}}[/tex]

Step 2 - Multiply numerator and denominator by [tex]a^2[/tex].

[tex]=\dfrac{-3a^{-2}b^3a^7}{15b^{-1}}\times \dfrac{a^2}{a^2}[/tex]

[tex]=\dfrac{-3b^3a^7}{15a^2b^{-1}}[/tex]

Step 3 - Multiply numerator and denominator by [tex]b^1[/tex].

[tex]=\dfrac{-3b^3a^7}{15a^2b^{-1}}\times \dfrac{b^1}{b^1}[/tex]

[tex]=\dfrac{-3b^3b^1a^7}{15a^2}[/tex]

Therefore, the correct option is B).

2).

Following steps can be use to determine the 2nd expression in positive exponents:

Step 1 - Multiply numerator and denominator by [tex]b^2[/tex].

[tex]=\dfrac{a^{3}b^{-2}}{ab^{-4}}\times\dfrac{b^2}{b^2}[/tex]

[tex]=\dfrac{a^{3}}{ab^{-4}b^2}[/tex]

Step 2 - Multiply numerator and denominator by [tex]b^4[/tex].

[tex]=\dfrac{a^{3}}{ab^{-4}b^2}\times\dfrac{b^4}{b^4}[/tex]

[tex]=\dfrac{a^{3}b^4}{ab^2}[/tex]

Therefore, the correct option is D).

3).

Following steps can be use to determine the 3rd expression in positive exponents:

Step 1 - Rewrite the given expression.

[tex]= \left[\dfrac{(4mn)^{-2}}{(m^{-2}n^{6})^{-2}}\right ][/tex]

Step 2 - Multiply numerator and denominator by [tex]\rm (4mn)^2\;and \;((m^{-2}n^6))^2[/tex].

[tex]=\left[\dfrac{(m^{-2}n^6)^2}{(4mn)^2}\right ]=\dfrac{m^{-4}n^{12}}{16m^2n^2}[/tex]

Step 3 - Multiply numerator and denominator by [tex]m^4[/tex].

[tex]=\dfrac{m^{-4}n^{12}}{16m^2n^2}\times\dfrac{m^4}{m^4}[/tex]

[tex]=\dfrac{n^{10}}{16m^6}[/tex]

Therefore, the correct option is B).

For more information, refer the link given below:

https://brainly.com/question/13911928