Simplify the expression ((3x^-4)(y^5)) / ((2x^3)(y^-7)^-2)
Please show work so I can see how to solve it, and briefly explain. Thanks. P.S. Because I have a feeling I'll be reprimanded: I am not having others do my homework. I'm studying; what I'm doing isn't even homework. An example just makes things easier to understand.
Please show work so I can see how to solve it, and briefly explain. Thanks. P.S. Because I have a feeling I'll be reprimanded: I am not having others do my homework. I'm studying; what I'm doing isn't even homework. An example just makes things easier to understand.
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Technicality, because technicalities are important! The word "solve" implies that you have an equation. Solving an equation means finding values which make the equation true. You didn't present an equation so using the word solve is meaningless.
Despite the title, you mean to simplify the expression. Simplifying an expression generally means to rewrite it in a form which is easier to understand or in a standard form. Let's give that a try.
I assume you mean to group things this way. (Hint: Be sure to include enough grouping symbols to make the meaning absolutely clear. You will notice I tend to add extra grouping symbols to make the calculations stand out.)
((3x^-4)(y^5)) / [ ((2x^3)(y^-7)^-2) ]
Factor out any constants that you can. Here we can factor out 3/2. (* means multiply.)
[3/2]*(x^-4)(y^5)/((x^3)(y^-7)^-2)
Simplify exponents as much as possible. Here (y^-7)^-2 becomes y^(-7*-2) or y^14.
[3/2]*(x^-4)(y^5)/((x^3)(y^14))
Combine exponents on variables:
[3/2]*(x^-4)(y^5)/((x^3)(y^14)
[3/2]x^(-4-3)y^(5-14)
[3/2]x^(-7)y^(-9)
Now we have to decide if simplifying means to remove negative exponents or fractions.
I actually prefer removing fractions so that the final answer is
[3/2]x^(-7)y^(-9)
If you prefer to make the exponents positive then you can convert it to a fraction like this
[3/2]/(x^7 * y*9) or 3/(2x^7y^9)
Technicality, because technicalities are important! The word "solve" implies that you have an equation. Solving an equation means finding values which make the equation true. You didn't present an equation so using the word solve is meaningless.
Despite the title, you mean to simplify the expression. Simplifying an expression generally means to rewrite it in a form which is easier to understand or in a standard form. Let's give that a try.
I assume you mean to group things this way. (Hint: Be sure to include enough grouping symbols to make the meaning absolutely clear. You will notice I tend to add extra grouping symbols to make the calculations stand out.)
((3x^-4)(y^5)) / [ ((2x^3)(y^-7)^-2) ]
Factor out any constants that you can. Here we can factor out 3/2. (* means multiply.)
[3/2]*(x^-4)(y^5)/((x^3)(y^-7)^-2)
Simplify exponents as much as possible. Here (y^-7)^-2 becomes y^(-7*-2) or y^14.
[3/2]*(x^-4)(y^5)/((x^3)(y^14))
Combine exponents on variables:
[3/2]*(x^-4)(y^5)/((x^3)(y^14)
[3/2]x^(-4-3)y^(5-14)
[3/2]x^(-7)y^(-9)
Now we have to decide if simplifying means to remove negative exponents or fractions.
I actually prefer removing fractions so that the final answer is
[3/2]x^(-7)y^(-9)
If you prefer to make the exponents positive then you can convert it to a fraction like this
[3/2]/(x^7 * y*9) or 3/(2x^7y^9)