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`

बेरीज

`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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पाठ 9: Indices - Exercise 9.1

पाठ 9 Indices
Exercise 9.1 | Q 6.5

Solve : 8 x 2^2x + 4 x 2^{x + 1} = 1 + 2^x

Solve:

2^2x + 2^x+2 − 4 × 2³ = 0

Find the values of m and n if :
`4^(2m) = ( root(3)(16))^(-6/n) = (sqrt8)^2`

Evaluate the following:

`(4^3 xx 3^7 xx 5^6)/(5^8 xx 2^7 xx 3^3)`

Evaluate the following:

`(27)^(2/3) xx 8^((-1)/6) ÷ 18^((-1)/2)`

Solve for x:
2^2x+3 - 9 x 2^x+ 1 = 0

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

If 2250 = 2^a. 3^b. 5^c, find a, b and c. Hence, calculate the value of 3^a x 2^-b x 5^-c.

If 2400 = 2^x x 3^y x 5^z, find the numerical value of x, y, z. Find the value of 2^-x x 3^y x 5^z as fraction.

If 2^x = 3^y = 12^z ; show that `(1)/z = (1)/y + (2)/x`.