Learn Exponents and Powers with Free Lessons & Tips

Solution:
To express the number in standard form, we move the decimal point to the right until there's only one non-zero digit to its left. The number of places we move the decimal point determines the power of 10.

0.00001275 m
= 1.275 × 10^(-5) m

So, the size of the plant cell in standard form is 1.275 × 10^(-5) meters.

Solution:
To find the thickness of 100 sheets, we multiply the thickness of one sheet by 100.

Thickness of 100 sheets = 0.0016 cm * 100

Now, let's perform the calculation:
= 0.0016 cm * 100
= 0.16 cm

Expressing the answer in standard form, we can write it as:
0.16 cm = 1.6 × 10^(-1) cm

So, the thickness of 100 sheets in standard form is 1.6 × 10^(-1) cm.

Problem:
Express the following numbers as powers of prime factors:

(i) 144
(ii) 225

Solution:
(i) Prime factorization of 144:
144 = 2^4 * 3^2

(ii) Prime factorization of 225:
225 = 3^2 * 5^2

So, the prime factorization of:
(i) 144 is 2^4 * 3^2
(ii) 225 is 3^2 * 5^2