how do i simplify this (-7a^-2 b^3 c^-1) ^-3i first put the questions under 1 i flipped the recirpocal so i could have a positive power of 3 so it looks like: 1 ___ 7a^2b^-3c^1) ^3 ..... and i...

how do i simplify this (-7a^-2 b^3 c^-1) ^-3

i first put the questions under 1 i flipped the recirpocal so i could have a positive power of 3 so it looks like:

1

___

7a^2b^-3c^1) ^3 ..... and i solve it but the answer is wrong

Expert Answers
hala718 eNotes educator| Certified Educator

You are not suppose to change the sign of (-7) when you flip. You only change the sign of the power.

Here how you simplify:

(-7a^-2 b^3 c^-1)^-3

= (-7a^-2)^-3 (b^3)^-3 (c^-1)^-3

= (-1/7^3) a^6 (b^-9) (c^3)

= -(a^6)(c^3)/343b^9

giorgiana1976 | Student

We just have to use the property of the negative power, which doues change only the sign of the exponents, not of the base, like this:

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

Let's take each term from the expression and to raise it to the negative power, applying the rule:

-7^(-3) = 1/(-7)^3 = -1/343

[a^(-2)]^(-3) = a^[(-3)*(-2)] = a^6

(b^3)^(-3) = b^(-9) = 1/b^9

[c^(-1)]^(-3) = c^[(-1)(-3)] = c^3

Now, let's re-write the expression, after the calculus:

(-1/343)*a^6*(1/b^9)*c^3 = -(a^6*c^3)/343*b^9

neela | Student

We use the index law:x^-n = 1/x^n

So (-7a^-2b^3c_1)^-3

= (-7/a^3 * b^3 * 1/c)^-3

= (7b^3/a^3 *c)^-3

= 1/(-7a^3*c)^3

= 1/{(-7a^3c){(-7a^3c){(-7a^3c)}

= 1/{-343a^(3+3+3)*c^(1+1+1)}

= -1/(343a^9  c^3)