Advertisements
Advertisements
Question
Prove the following:
`(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ (x^"q"/x^"p")^"r"` = 1
Advertisements
Solution
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
RELATED QUESTIONS
Solve for x : 22x+1 = 8
Find x, if : 42x = `1/32`
If m ≠ n and (m + n)-1 (m-1 + n-1) = mxny, show that : x + y + 2 = 0
If 5-P = 4-q = 20r, show that : `1/p + 1/q + 1/r = 0`
Solve : 3x-1× 52y-3 = 225.
Evaluate the following:
`(12^2 xx 75^-2 xx 35 xx 400)/(48^2 xx 15^-3 xx 525)`
Solve for x:
22x+1= 8
If x = `3^(2/3) + 3^(1/3)`, prove that x3 - 9x - 12 = 0
Prove the following:
`sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)` = 1
Prove the following:
`root("ab")(x^"a"/x^"b")·root("bc")(x^"b"/x^"c")·root("ca")(x^"c"/x^"a")` = 1
