Simplify the Following: 3 X + 1 + 3 X 3 X + 3 − 3 X + 1 - Mathematics

Simplify the following:

`(3^(x + 1) + 3^x)/(3^(x + 3) - 3^(x + 1)`

Sum

`(3^(x + 1) + 3^x)/(3^(x + 3) - 3^(x + 1)`

= `(3^x (3 + 1))/(3^x(3^3 - 3)`

= `(4)/(27 - 3)`

= `(4)/(24)`

= `(1)/(6)`.

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Simplification of Expressions

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 8.2

If 3^4x = ( 81 )^-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `

Solve : 3(2^x + 1) - 2^x+2 + 5 = 0.

If (a^m)ⁿ = a^m .aⁿ, find the value of : m(n - 1) - (n - 1)

Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`

Prove that: `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = (2b^2)/(b^2 - a^2 )`

Simplify : a² − 2a + {5a² − (3a - 4a²)}

Write each of the following in the simplest form:
(a³)⁵ x a⁴

Write the following in the simplest form:
(b^-2 - a^-2) ÷ (b^-1 - a^-1)

Simplify the following:

`((64"a"^12)/(27"b"^6))^(-2/3)`

Simplify the following:

`((36"m"^-4)/(49"n"^-2))^(-3/2)`