Question

evaluate .exponents and powers 8th standard
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Answer 1

FACTS THAT MATTER

• The numbers with negative exponents also obey the following laws:

(i) xm × xn = xm + n

(ii) xm ÷ xn = xm – n

(iii) xm × bm = (xb)m

(ii) x0 = 1

• A number is said to be in the standard Form, if it is expressed as the product of a number between 1 and 10 and the integral power of 10.

• Very small numbers can be expressed in standard form using negative exponents.

WE KNOW THAT

When we write 54, it means 5 × 5 × 5 × 5, i.e. 5 is multiplied 4 times. So 5 is the base and 4 is the exponent. We read 54 as �5 raised to the power 4�.

We also know the following laws of exponents

(i) xm × xn = xm + n

(ii) xm ÷ xn = xm – n

(iii) xm)n = xm × n

(iv) xm × ym = (xy)m

The value of any number raised to 0 is 1, i.e. a0 = 1.

We express very small or very large numbers in standard form (i.e scientific notation) for example:

POWER WITH NEGATIVE EXPONENTS

For a non-zero integer x, we have

or x�m × xm = 1

So x�m is the reciprocal (or the multiplicative inverse) of xm and vice versa.

For example: (i) Reciprocal of 8�7 = 87 and

(ii) Reciprocal of 87 = 8�7