Advertisements
Advertisements
प्रश्न
Prove the following:
`(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ (x^"q"/x^"p")^"r"` = 1
Advertisements
उत्तर
L.H.S
= `(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ (x^"q"/x^"p")^"r"`
= `(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ x^"qr"/x^"pr"` .....(Using (am)n = amn)
= `(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) xx x^"pr"/x^"qr"`
= `(x^("pq"-"pr"))/x^("pq"- "qr") xx x^"pr"/x^"qr"`
= `(x^("pq"-"pr"+"pr"))/(x^("pq"-"qr"+"qr"` .....(Using am x an = am+n)
= `(x^("pq"))/(x^("pq")`
= 1
= R.H.S
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find x, if : `sqrt( 2^( x + 3 )) = 16`
Solve : `[3^x]^2` : 3x = 9 : 1
Solve for x:
`(81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27`
If ax = b, by = c and cz = a, prove that : xyz = 1.
Solve x and y if : ( √32 )x ÷ 2y + 1 = 1 and 8y - 164 - x/2 = 0
Solve for x:
22x + 2x +2 - 4 x 23 = 0
Find the value of k in each of the following:
`(sqrt(9))^-7 xx (sqrt(3))^-5` = 3k
Find the value of 'a' and 'b' if:
92a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`
Prove the following:
`sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)` = 1
Prove the following:
`("a"^"m"/"a"^"n")^("m"+"n"+1) ·("a"^"n"/"a"^1)^("n" + 1-"m").("a"^1/"a"^"m")^(1+"m"-"n")`
