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Question

Simplify 2(to the power -1) × 27(to the power 2/3), giving the answer as interger or fraction.

Answer 1

2^(-1)*27^(2/3)=9/2

Answer 2

To do this, start by considering 27^(2/3). Now, when you have an expression of the form x^(1/n), where n is a positive integer, this means the same thing as "the nth root of x".

So, 27^(2/3) = (27^(1/3))^2, by rules of indices. However, note that 27^(1/3) means the cube root of 27. Now, 3x3x3=9x3=27. Thus 3 is the cube root of 27.

Now, substituting this back into the equation, we get:

2^(-1)x(3^2)
2^(-1)x9
Now, if you have an expression of the form x^(-n), where n is a positive integer, then this is the same as (1/x)^n. So
2^(-1)x9=9/2

Answer 3

The tricky part is 27(to the power 2/3).
27 to 1/3 is 3.
27 to 2/3 is 3 x 3 of 27 = 9.
27 to 3/3 is 27 to the power of one = 27

So without a calulator the answer = 2 x 9 = 18

Answer 4

4.5

2 to the power -1 = 1/2
27 to the power 2/3 = (cube root of 27)^2 = 3^2 = 9
1/2 × 9 = 9/2 or 4.5

Answer 5

2^-1 * 27^2/3 = 1/2 * cube root of 27^2 = 1/2 * 9 = 9/2 = 4 1/2

Answer 6

to the power -1 means 1 over

= 1/2 x 27^2/3
to the power 2/3 is cube root and square it
= 1/2 x (cube root)27squared
= 4.5
= 9/2

Answer 7

2^(-1) x 27^(2/3)
= (1/2) x Cube root of (27)^2
= (1/2) x 3^2
= (1/2) x 9
= 4.5 or 4 1/2

Answer 8

9/2

Answer 9

2^-1=1/2
27^2/3=(quebed root of 27)^2
so its 1/2 x 3^2
=1/2 x 9
=4.5

Answer 10

{(2^(-1)*(27)^(2/3)} = (1/2)*{27^2}^(1/3)
={cube root(27*27)}/2
={3*3}/2=9/2

i hope that this helps