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100 POINTS!!!!! PLEASE HELP!

100 POINTS!!!!! PLEASE HELP!-example-1
User EMIN
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2 Answers

5 votes

Answer:


a^(12)\:b^(4)

Explanation:

Given expression:


\left(a^(-4)\:b^(-1)\:c\right)^(-2)\left(a^2\:b\:c\right)^2


\textsf{Apply exponent rule} \quad (a^b)^c=a^(bc):


\implies a^((-4 * -2))\:b^((-1 * -2))\:c^(-2)\:a^((2 * 2))\:b^2\:c^2

Simplify:


\implies a^(8)\:b^(2)\:c^(-2)\:a^(4)\:b^2\:c^2

Collect like terms:


\implies a^(8)a^(4)\:b^(2)b^2\:c^(-2)c^2


\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^(b+c):


\implies a^((8+4))\:b^((2+2))\:c^((-2+2))

Simplify:


\implies a^(12)\:b^(4)\:c^(0)


\textsf{Apply exponent rule} \quad a^0=1:


\implies a^(12)\:b^(4)(1)


\implies a^(12)\:b^(4)

User Sondergaard
by
8.5k points
5 votes

Answer:


a^(12) b^(4)

Explanation:

To simplify we will have to use the negative exponent rule and the power rule along with some algebra.

Negative Exponent Rule


a^(-b) =(1)/(a^b)

Power Rule


(a^b)^(c) =a^(bc)

Given


(a^(-4)b^(-1)c )^(2) (a^2bc)^(2)

Rewrite
a^(-4) using negative exponent rule.


((1)/(a^(4))* b^(-1)c )^(2) (a^2bc)^(2)

Rewrite
b^(-1) using negative exponent rule.


((1)/(a^(4))* (1)/(b)*c )^(2) (a^2bc)^(2)

Simplify


((c)/(a^4b) )^(2) (a^2bc)^(2)

Rewrite the base as its reciprocal.


((a^4b)/(c) )^(2) (a^2bc)^(2)

Apply the power rule.


(a^8b^2)/(c^2) *(a^2bc)^(2)

Apply the power rule.


(a^8b^2)/(c^2) *a^4b^2c^2

Cancel the common factor of
c^2.


a^8b^2 a^4b^2

Apply the power rule.


a^(12) b^(4)

User Cettt
by
8.3k points

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