Rational exponents(powers) of a number

Exponent of any number in n!

laws of Rational exponents are same as real exponents.(i) a^(p)xx a^(q)=a^(p+q)( ii) (a^(p))/(a^(q))=a^(p-q) (iii) (a^(p))^(q)=a^(pq)( iv )a^(-q)=(1)/(a^(q))

Use of exponents to express small numbers in standard form

Express each of the following products of powers as the exponent of a rational numbers: (i) 2^5xx3^5 (ii) (-4)^3xx(-2)^3 (iii) 3^7xx(-2)^7

Exponent of a prime number in n!!

If x is a positive real number and the exponents are rational numbers,show that: ((x^(a))/(x^(b)))^(a+b-c)((x^(b))/(x^(c)))^(b+c-a)((x^(c))/(x^(a)))^(c+a-b)=1

Exprtess the following as the power of a rational number. (16)/(81)