Question

"Question 2 Simplify and express the result in power notation with positive exponent.
(i) (-4)^5 / (-4)^8

(ii) (1/2^3)^2

(iii) (-3)^4 x (5/3)^4

(iv) [ 3^(-7) / 3^(-10) ] x 3^(-5)

(v) 2^(-3) x (-7)^(-3)

Class 8 Exponents and Powers Page 197"

Answer 1

An exponent on index is a number written to the right and the little above the base. It indicates the number of times the base occurs in the product.

For e.g

X² it is read as X squared or X raised to the power 2 or X to the power 2.

Here X is the base & 2 is the exponent or index.

·        If p/q is a rational number and m is a positive integer then (p/q)^m = p^m/q^m

·        If x be any rational number and m, n be any  integers then x^m × x^n= x^m+n

·        If x be any non zero rational number and m,n be any positive integers such that m>n ,then x^m ÷ x^n= x^m-n

·        If x be any non zero rational number and m,n be any positive integers such that m<n ,then x^m ÷ x^n= 1/ x^n-m

·        If x be any non zero rational number then x^0= 1

·        If x be any non zero rational number then x-¹= 1/x

·        If x be any non zero rational number & m be any positive Integer then x^-m=1/x^m

·        If x be any non zero rational number & m,n be any positive Integer then( x^m)^n= x^mn.

·        If x be any non zero rational number & m be any positive Integer then x^m × y^ m=(XY)^m

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Solution is in the attachment

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Hope this will help you....

Answer 2

Step-by-step explanation:

1) 1/(-4)^3

2) 1/2^6

3) 5^4

4) 1/3^2

5) 1/(-14)^3