I need an explanation on how to work out
negative exponents. Example: (3a^-2b^3)^-2
(3a^-2b^3)^-2 =
1/(3a^-2*b^3)2 =
Square everything inside the parenthesis:
1/(9a^-4*b^6) = a^4/9b^6.
NOTE: Never leave neg. exponents in your answer. To remove the neg. exponent
from 1/a^-4, multiply numerator and
denominator by a^4:
1/a^-4 = 1*a^4/a^-4*a^4 = a^4/1 = a^4.
We,actually, moved a^-2 to the numerator
and changed the sign.
Correction: We,actually, moved a^-4 to
the numerator and changed the sign of the exponent.
To work out negative exponents, you can follow these steps:
Step 1: Start by applying the negative sign to the exponent inside the parenthesis, taking the reciprocal of the base.
For the given example, (3a^-2b^3)^-2, we have a negative exponent -2 inside the parenthesis. Applying the negative sign, we invert the base and change the exponent to positive:
(3a^-2b^3)^-2 = (1 / 3a^2b^3)^2
Step 2: Simplify what's inside the parenthesis, raising everything to the power outside the parenthesis. Follow the exponent rules, such as multiplying exponents when raising a power to a power.
In this case, we have (1 / 3a^2b^3)^2. To simplify, we raise both the numerator and the denominator to the power of 2:
(1^2) / (3a^2b^3)^2 = 1 / (3^2 * a^2 * b^6)
Step 3: Simplify the expression further, performing any necessary calculations.
Continuing to simplify, we square the values of 3, a, and b:
1 / (3^2 * a^2 * b^6) = 1 / (9 * a^2 * b^6)
So, the simplified expression for (3a^-2b^3)^-2 is 1 / (9 * a^2 * b^6).