What is the simplified form of each expression?
1) 3g^-2b^2
A)3b^2/g^2
B)3g^2b^-2
C)3gb^-4***
D)b^2/3g^2
2) 3/g^-2h^3
A)3/g^2h^3***
B)3g^2/h^3
C)6g/h^3
D)3/gh
Are these correct? If not, please explain.
Someone please help me???
3 g^-2 b^2
g^-2 = 1/g^2
so, the expressions is the same as
3b^2/g^2
1/g^-2 = 1/(1/g^2)) = g^2
Now we get into murky waters:
(3/g^-2)h^3 = 3g^2h^3 -- not a choice
3/(g^-2h^3) = 3g^2/h^3
because that is the same as
3 * 1/g^-2 * 1/h^3 = 3g^2/h^3
don't be afraid to use parentheses online, where text formatting is usually rudimentary
Ok, okay, thank you so much! (=
To simplify the given expressions, we can apply the rules of exponents. Let's break it down step by step:
1) 3g^-2b^2
To simplify this expression, we need to consider the negative exponent. When a term has a negative exponent, it can be flipped to the denominator of a fraction. So, we can rewrite it as:
3(b^2 / g^2)
Now, the expression is simplified by putting the terms with the same base together. Therefore, the simplified form is:
3b^2 / g^2
So, option A) 3b^2 / g^2 is the correct answer.
2) 3 / g^-2h^3
Again, we need to deal with the negative exponent first. The term g^-2 can be flipped to the denominator as g^2. So, we have:
3 / (g^2h^3)
Now, we can rewrite it as a fraction:
3/g^2h^3
Hence, option A) 3 / g^2h^3 is the correct answer.
In summary, both of your answers are correct.