Calculate the value of the following in exponential form, using standard scientific or "e" notation (for example, 105 = 1.05e2). Enter the correct number of significant figures.

(2.700e2 cm)3 / (1.20e3 cm)2

Can't understand how many sig figs.

I think the brackets might be in the wrong place for the units, however..

...the significant figures in the answer are determined by the minimum number of sig figs in the division. By putting the values into scientific notation the sig figs are obvious, which they are not when the values are written out in full.

2.700e2 cm3 4 sig figs

1.20e3 cm2 3 sig figs

so the answer should be to 3 sig figs as this is the smallest number of sig figs in the division.

I'll leave to sort out is the calculation is really

(2.700e2 cm)3 / (1.20e3 cm)2

or

2.700e2 cm3 / 1.20e3 cm2

21.8

To determine the number of significant figures in the final answer, we need to consider the significant figures in each component of the expression.

For the numerator, "2.700e2 cm", we have three significant figures (2, 7, and 0). The exponent "e2" does not affect the significant figures.

For the denominator, "1.20e3 cm", we have three significant figures (1, 2, and 0). The exponent "e3" does not affect the significant figures.

Now, let's calculate the value:

(2.700e2 cm)^3 / (1.20e3 cm)^2

First, let's simplify the numerator and denominator:

(2.700e2 cm)^3 = (2.700e2)^3 cm^3 = 2.700^3 e2^3 cm^3 = 19.683e6 cm^3
(1.20e3 cm)^2 = (1.20e3)^2 cm^2 = 1.44e6 cm^2

Next, let's perform the division:

19.683e6 cm^3 / 1.44e6 cm^2 = 19.683 / 1.44 e6 cm^3 / cm^2 = 13.625 e6 cm

Now, let's put the answer in standard scientific notation ("e" notation) with the correct number of significant figures:

13.625e6 cm

Considering the significant figures in the numerator and denominator, we have three significant figures in the numerator but only two in the denominator. To comply with the rule of significant figures, the final answer should have two significant figures, which are "13.625".

4.21