+1-415-670-9189

info@expertsmind.com

# Indices, Laws to Indices, Math Assignment Help

###
mathematics - Indices, Laws to Indices, Math

**INDICES**

If a be any real number and n is the natural number, then

a^{n }= a × a × a x ..... × a n factors and n is index of a and plural of index is indices.

**Laws to Indices: **

(i) a^{m} × a^{n} = a^{m+}^{¸}^{n }; a Î R^{+}, m, n, Î N

(ii) a^{m} ¸ a^{n} = a^{m-n} ,a Î R^{+}, m, n, Î N

(iii) (a^{m})^{n} = a^{mn }; a Î R^{+}, m, n. Î N

(iv) (ab)^{n} = a^{n}b^{n}; ab Î R, n Î N

(v) (a ¸ b)^{n} = an + b^{n} = b^{n } = a^{n}/b^{n}; a, b Î R^{+}, n Î N

(vi) a^{0} = 1, Where a is non-zero real number

(vii) a-^{n} = 1/a^{n}; a Î R, n a non-negative.

(viii) If a and b are two positive real numbers and n a natural number, such that b^{n} = a, then b = a^{1/n}.

(ix) If a is a positive real number and m and n are integers with n positive, then (1/a^{n})^{m} a^{m/n}

(x) If a, b are positive real numbers and n a natural number, then

a^{n/2} b^{n/2 }= (ab)^{n/2}

(xi) If a^{m} = b^{m}, then a = b

(xii) If a^{m} = a^{n}, then m = n.

**Indices, Laws of Indices, Math Homework Help**

Expertsmind.com offers indices and laws of indices basic math homework help, assignments help and online tutorial with assistance of qualified and experienced expert tutors. Our math experts make easy solution for you in indices related mathematics problems by giving you step by step answers which helps you in future to solve same kind of problems. Get instant math help from qualified tutors at Expertsmind.com anytime from any where.

**INDICES**

^{n }= a × a × a x ..... × a n factors and n is index of a and plural of index is indices.

**Laws to Indices:**

^{m}× a

^{n}= a

^{m+}

^{¸}

^{n }; a Î R

^{+}, m, n, Î N

^{m}¸ a

^{n}= a

^{m-n},a Î R

^{+}, m, n, Î N

^{m})

^{n}= a

^{mn }; a Î R

^{+}, m, n. Î N

^{n}= a

^{n}b

^{n}; ab Î R, n Î N

^{n}= an + b

^{n}= b

^{n }= a

^{n}/b

^{n}; a, b Î R

^{+}, n Î N

^{0}= 1, Where a is non-zero real number

^{n}= 1/a

^{n}; a Î R, n a non-negative.

^{n}= a, then b = a

^{1/n}.

^{n})

^{m}a

^{m/n}

^{n/2}b

^{n/2 }= (ab)

^{n/2}

^{m}= b

^{m}, then a = b

^{m}= a

^{n}, then m = n.

**Indices, Laws of Indices, Math Homework Help**