Advertisements
Advertisements
प्रश्न
State the product law of exponents.
Advertisements
उत्तर
State the product law of exponents.
If a is any real number and m,n are positive integers, then
`a^m xx a^n = a^(m+n)`
By definition, we have
`a^m xx a^n = (a xx a xx ...m " factor") xx (a xx a xx ...n "factor")`
`a^m xx a^n = a xx a xx..... "to " (m+n)` factors
`a^m xx a^n = a^(m+n)`
Thus the exponent "product rule" tells us that, when multiplying two powers that have the same base, we can add the exponents.
APPEARS IN
संबंधित प्रश्न
Solve the following equation for x:
`2^(5x+3)=8^(x+3)`
Solve the following equation for x:
`2^(3x-7)=256`
Given `4725=3^a5^b7^c,` find
(i) the integral values of a, b and c
(ii) the value of `2^-a3^b7^c`
Find the value of x in the following:
`5^(x-2)xx3^(2x-3)=135`
If a and b are different positive primes such that
`((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y,` find x and y.
Write the value of \[\left\{ 5( 8^{1/3} + {27}^{1/3} )^3 \right\}^{1/4} . \]
Which of the following is (are) not equal to \[\left\{ \left( \frac{5}{6} \right)^{1/5} \right\}^{- 1/6}\] ?
The simplest rationalising factor of \[2\sqrt{5}-\]\[\sqrt{3}\] is
If \[\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}, \text { then a } =\]
Find:-
`32^(1/5)`
