Find the simplified form of each expression
(3/5y^4)^-2
(all of this is in parenthese except the exponent at the very end)
please help.
I also has a similar problem which is (3/2b^4)^3
But for this one, since it is a positive exponent, (i don't do well with negatives)
can someone please guide me through what i have to do WITHOUT giving me the answer, BC i wanna try this on my own, but don't know where to start.
To simplify the first one you need to get rid of the outside exponent. You multiply 3/5 by 2. (You flip the fraction and that gets rid of the negative.)
Then you simply multiply 4 and -2.
Don't forget to keep the y!
For the second one, you multiply 3/2 by 3 and then multiply 4 by 3.
Don't forget the b!
Let me know if that helps at all.😀
It did! Thanks a bunch!
To simplify the expression (3/5y^4)^-2, we need to understand the rules of exponents.
The rule for a negative exponent is that any number or variable raised to a negative exponent can be written as its reciprocal with a positive exponent. That is, a^(-n) = 1/a^n.
Applying this rule to our expression:
(3/5y^4)^-2 = 1/(3/5y^4)^2
Next, we need to apply the rule for raising a power to a power. The rule states that (a^m)^n = a^(m*n). Using this rule:
1/(3/5y^4)^2 = 1/(3/5)^2 * (y^4)^2
Now, let's simplify the parts separately. First, we calculate (3/5)^2, which is equal to (3^2)/(5^2) = 9/25.
Next, we simplify (y^4)^2. When raising a power to another power, we multiply the exponents. Therefore, (y^4)^2 = y^(4*2) = y^8.
Substituting these simplified parts back into the expression:
1/(3/5y^4)^2 = 1/(9/25 * y^8)
To divide fractions, we multiply the numerator by the reciprocal of the denominator. So:
1/(9/25 * y^8) = 1 * (25/9 * 1/y^8)
Multiplying across, we get:
1 * (25/9 * 1/y^8) = 25/(9y^8)
Therefore, the simplified form of the expression (3/5y^4)^-2 is 25/(9y^8).