Question

Express -32/243 into power notation​

Answer 1

The fraction -32/243 can be expressed in power notation as - (2/3)^5, with the negative sign indicating that the number is negative.

Step-by-step explanation:

To express the fraction -32/243 in power notation, we can observe that both the numerator and denominator are powers of 2 and 3, respectively. Since 32 is 2 to the 5th power (25) and 243 is 3 to the 5th power (35), we can write the fraction as:

(-25)/(35)

Recognizing that when we divide two numbers with the same exponent we can subtract the exponents, we apply the rule of negative exponents for division:

(-1)(2/3)5 or - (2/3)5

The negative sign remains to show that the value is negative. Here, we are using base 2/3, which is raised to the power of 5, and the negative sign indicates the fraction is negative.

Answer 2

This problem can take a while if you cannot observer the answer quickly.

First of all we can see that 32=2*2*2*2*2=2^5

243, if you don't know its actually is 3^5

Now we can see that this turns into...

- 2^5/3^5

since the 5th power doesn't change the sign of the original number, we can put the negative in the ( ), if you don't know what I mean look below

(-3)^2=9 Positive

(-3)^3=-27 Negative since its to the odd power it keeps the sign.

This problem can be simplified to.

(-2/3)^5

And this is the answer :D

If you have any questions just put them in the comments.