Question

The value of [ 9^ (n+ 1/4) (√3.3^n) / 3. √(3) ^-n ] 1/n​

Answer 1

Answer:

27

Step-by-step explanation:

refer the photo, the perfect answer

Answer 2

The answer is $27^{n}$.

• A number's exponents signifies how many times the number has been multiplied by itself. It also says how many times we must multiply the reciprocal of the base is indicated by a negative exponent. A fractional exponent is one where the exponent of a number is a fractional number. A number's exponent is referred to as a the exponent of a decimal if it is expressed in decimal form.
• Any decimal exponent's proper response can be a little tricky to evaluate, thus in these situations, we calculate the approximate solution. The preferred method for writing extremely large or extremely small integers is known as scientific notation. Here, powers of ten and the decimal system are used to write numerals.

Here, according to the given information, we are given that,

The expression is,

$\frac{9^{n+\frac{1}{4} .\sqrt{3.3^{n} } } }{3.\sqrt{3^{-n} } }$

Now, we get,

$\frac{9^{n+\frac{1}{4}.3^{n} .\sqrt{3 } } }{3} }$

Now, we have that 9 is the square of 3.

Then, we get,

$3^{2n+\frac{1}{2}.3^{n-1} .3^{\frac{1}{2} } } }$

Now, by the rules of exponents, adding the powers of 3, we get,

$3^{2n+n-1+1 }$

Or,

$3^{3n} \\=27^{n}$

Hence, the answer is $27^{n}$.

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