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

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 9: Indices - Exercise 9.1

अध्याय 9 Indices
Exercise 9.1 | Q 6.5

Solve : 4^{x - 2} - 2^{x + 1} = 0

Solve for x:
`9 xx 3^x = (27)^(2x - 5)`

Solve for x:
p³ x p^-2 = p^x

Solve for x:
5^x2 : 5^x= 25 : 1

Solve for x:
9^x+4= 3² x (27)^x+1

If a = `2^(1/3) - 2^((-1)/3)`, prove that 2a³ + 6a = 3

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")`

Prove the following:

`root("ab")(x^"a"/x^"b")·root("bc")(x^"b"/x^"c")·root("ca")(x^"c"/x^"a")` = 1

Prove the following:
(x^a)^b-c x (x^b)^c-a x (x^c)^a-b= 1