Question

State true or false. Correct the statement in case the answer is false.
a) 1 mm equals 100000000 km
c) 10000000 can be written as 3 x 10-7
d) Ifp is a rational number and m and n are the integers, then p-p"=p"*"
e) Ifp and q are rational numbers and m is an integer, then p" x 9" = (p9)​

Answer 1

Given :-

a) 1 mm equals 1/100000000 km .

• False .

→ 1 km = 1000 m

→ 1 m = 100 cm

→ 1 cm = 10 mm

so,

→ 1 km = 1000 * 100 * 10 = 1000000 mm

then,

→ 1 mm = (1/1,000,000) km .

b) 3/19 = (19/3)^(-1)

• True .

solving RHS,

→ (19/3)^(-1)

using a^(-m) = 1/a^m

→ 1/(19/3)¹

→ (3/19) = LHS .

c) 3/10000000 can be written as 3 x 10^(-7)

• True .

d) If p is a rational number and m and n are the integers, then p^m ÷ p^n =p^(m + n)

• False .

→ p^m ÷ p^n =p^(m - n)

e) If p and q are rational numbers and m is an integer, then p^m x q^m = (pq)^m

• True .

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