math help??

Question

(243 ^ -1/3) ^ -3/5

is it
a) 27
b) -27
c) -3
d) 3

please show me how to do it

Answer 1

(243^-1/3)^-3/5

= 243^3/15

= (3^5)^3/15

= 3^15/15

=3^1

=3

Answer is ''d)''

Answer 2

243 ^ -1/3 = 1/ (the cube root of 243)
1/ (the fifth root of the answer we got in the last step) ^3

A negative exponent means to find the reciprocal or simply to divide 1 by the number.

A fraction as an exponent means find the exponent's denominator and that will be the root of the number then find the numerator of the exponent and use it like a normal exponent.

So the answer is 3

Answer 3

the answer is d.
When a number that is taken to an exponent is taken to another exponent, they are multplied together. So -1/3 is multiplied by -3/5. This gives you 1/5. So then its 243^1/5, which is 3.

Answer 4

(243^-1/3)^-3/5 =
243^1/5 (multiply the two exponents -1/3 * -3/5 = 1/5
Now take the 5th root of 243, which is 3

Answer 5

Since one exponent is inside the parentheses and the other is outside, you multiply the two. This makes it a lot simpler already, since the two negatives make a positive. Then it should be pretty easy to figure out which one of the choices multiplied by itself x number of times will equal the base number.

Answer 6

[(243)^-(1/3]^(-3/5)
=[243]^(-1/3)(-3/5) (since (a^x)^y = a^(xy))
=[243]^(1/5)
=[3^5]^(1/5)
=[3]^[(5)*(1/5)]
=3^1
=3

Answer 7

I'm not sure how to do it by hand, but you could just type it into your calculator. (make sure you include the parentheses)

Answer 8

d

Answer 9

What the hell are these> ^ ?