State whether the given statements are True or False.xm × xn = xm + n, where x is a non-zero rational number and m,n are positive integers.

According to Law of indices,am × an = a (m + n)xm × xn = xm + nSo the statement is true.

Q54 of 111 Page 337

State whether the given statements are True or False.
x^m × xⁿ = x^{m + n}, where x is a non-zero rational number and m,n are positive integers.

According to Law of indices,

a^m × aⁿ = a ^{(m + n)}

x^m × xⁿ = x^{m + n}

So the statement is true.

State whether the given statements are True or False.

x^m × y^m = (x × y)^2m, where x and y are non-zero rational numbers and m is a positive integer.

State whether the given statements are True or False.

x^m ÷ y^m = (x ÷ y)^m, where x and y are non-zero rational numbers and m is a positive integer.

State whether the given statements are True or False.

4⁹ is greater than 16³.

State whether the given statements are True or False.