Help please....Please Simplify
(-3a^-5 b^6)^4 (a^7b^0)^3
any ideas? thanks in advance!
First, I will assume that the -3 at the beginning will not be raised to the -5th power.
A little revision of the law of indices is in order:
(ab)^n = a^n . b^n
this will apply to the ^4 and ^3 outside of the parentheses.
a^-n=1/a^n
This will apply to the term a^-5
b^0 = 1
for all values of b except 0.
(-3a^-5 b^6)^4 (a^7b^0)^3
=(-3b^6/a^5)^4 (a^7 . 1)^3
=(-3)^4 (b^6)^4 /(a^5)^4 (a^7)^3
= (-3)^4 (b^24)/(a^20) (a^21)
= ...
I will let you take it from here.
Post your answer for a check if you wish.
=
Ok thanks! I got 81ab^24 Is this correct? Thanks!
Excellent, the answer is correct.
Do start the problem over to understand every step.
To simplify the expression (-3a^-5 b^6)^4 (a^7b^0)^3, we can apply the exponent rules for multiplication and division.
First, let's simplify (-3a^-5 b^6)^4:
To raise a power to a power, we multiply the exponents. In this case, the exponent of -5 is being raised to the power of 4, so the new exponent will be -5 * 4 = -20. Similarly, the exponent 6 is being raised to the power of 4, resulting in 6 * 4 = 24.
Thus, we simplify (-3a^-5 b^6)^4 to (-3^4 a^-20 b^24).
Now let's simplify (a^7b^0)^3:
Any number or variable raised to the power of 0 is equal to 1, so b^0 = 1. Therefore, (a^7b^0)^3 simplifies to (a^7)^3.
To simplify further, we need to apply the exponent rule for multiplication. When multiplying two powers with the same base, we add the exponents. So (-3^4 a^-20 b^24) * (a^7)^3 simplifies to -3^4 * a^-20 * b^24 * a^21.
Recall that a negative exponent indicates reciprocal. Therefore, a^-20 can be written as 1/a^20.
Simplifying further, we have -3^4 * (1/a^20) * b^24 * a^21.
Calculating the exponents, -3^4 = -81, 1/a^20 remains the same, and b^24 * a^21 can be written as (ba)^21.
Thus, the simplified expression is -81 * (1/a^20) * (ba)^21, or -81/a^20 * (ba)^21.