Evaluate the Following: 16 3 4 + 2 ( 1 2 ) − 1 × 3 0

Evaluate the following:

`16^(3/4) + 2(1/2)^-1 xx 3^0`

योग

`16^(3/4) + 2(1/2)^-1 xx 3^0`

= `2^(4 xx 3/4) + 2 xx 2 xx 1`
= 2³ + 4
= 2³ + 4
= 8 + 4
= 12.

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Solving Exponential Equations

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अध्याय 6: Indices - Exercise 9.1

अध्याय 6 Indices
Exercise 9.1 | Q 6.5

Find x, if : 4^2x = `1/32`

Solve for x:

`(81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27`

Solve for x : 3(2^x + 1) - 2^{x + 2} + 5 = 0

If 5^-P = 4^-q = 20^r, show that : `1/p + 1/q + 1/r = 0`

If a^x = b^y = c^z and b² = ac, prove that: y = `[2xz]/[x + z]`

If `((a^-1b^2 )/(a^2b^-4))^7 ÷ (( a^3b^-5)/(a^-2b^3))^-5 = a^x . b^y` , find x + y.

Evaluate the following:

`9^(5/2) - 3 xx 5^0 - (1/81)^((-1)/2)`

Solve for x:
p³ x p^-2 = p^x

Show that : `(1)/(1 + "a"^("p"- "q")) + (1)/(1 + "a"^("q"- "p")`

Prove the following:

`(x^("a"+"b")/x^"c")^("a"-"b") · (x^("c"+"a")/(x^"b"))^("c"-"a") · ((x^("b"+"c"))/(x"a"))^("b"-"c")` = 1