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How to do this question?

(27/8)^-2/3

This is on a past paper and its confusing. If this comes up in the exam tomorrow im f'd. Could someone give me the answer to this please.

I think is it 1/(2squareroot27/8)^3

Reply 1

F35-LII

flip and divide by the powers, answer is 4/9

Reply 2

Gemini92

Original post by alai.y

(27/8)^-2/3

This is on a past paper and its confusing. If this comes up in the exam tomorrow im f'd. Could someone give me the answer to this please.

I think is it 1/(2squareroot27/8)^3

You have to cube root, square and take the reciprocal on the fraction (order doesn't matter), so you should get 4/9.

Reply 3

Bobifier

The minus indicates that it will be 1/ something. You treat the numerator of the fraction as a power and the denominator as a root, so it is 1 divided by the third (i.e. the cube) root of (27/8)^2. Note that it doesn't matter whether you take the root of the square or the square of the root, they are the same number.

Reply 4

The Mr Z

Original post by alai.y

(27/8)^-2/3

This is on a past paper and its confusing. If this comes up in the exam tomorrow im f'd. Could someone give me the answer to this please.

I think is it 1/(2squareroot27/8)^3

answer is 4/9

seperate the powers out to make it more obvious:

(\frac{(27^(\frac{1}{3}))^2}{(8^(\frac{1}{3}))^2})^{-1}

(this isn't displaying too well)

a^(1/3) = cube root of a
cube root of 27=3, cube root of 8 = 2

then ^2 is squaring: 3^2 = 9, 2^2 =4

finally, all to the power of -1 means invert the fraction