Question

One terameter equals 1012 meters. One micrometer equals 10 meter.

One nanometer equals 10-9 meter.

a. Find the product of one terameter and one micrometer,

using only positive exponents.

b. Find the quotient of one terameter and one micrometer,

using only positive exponents.

Answer 1

a) 10⁶metres

b) 10¹⁸metres

Explanation:

Given One terameter equals 10¹² meters. One micrometer equals 10⁻⁶ meter, one nanometer equals 10⁻⁹meter;

a) The product of one terameter and one micrometer will be expressed as;

10¹² * 10⁻⁶

Since the both have the same base, we will add their power according to one of the law in indices as shown

10¹² * 10⁻⁶ = 10⁻⁶⁺¹²

= 10⁶metres

b) The quotient of one terameter and one micrometer can be gotten by taking their ratio as shown below;

Note that when taking the quotient, the power are subtracted

`= (10^(12) )/(10^(-6) ) \\= 10^(12-(-6)) \\= 10^(12+6) \\= 10^(18)metres`