Maths-

General

Easy

Question

# Evaluate as a fraction (64 / 27)^{2/3} − (1/9)^{−2} + 9^{0}

Hint:

### In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.

an = a × a × ... × a n times.

## The correct answer is: Value of given expression, when simplified is -208/9 or -23.11.

### Step-by-step solution:-

(64/27)^{2/3} − (1/9)^{−2} + 9^{0}

= (2^{6}/3^{3})^{2/3} - (9)^{2} + 1 …................................................. (b^{-n}= 1/b^{n} & b^{0} = 1)

= 2^{6×3/2} / 3^{3×2/3} - 81 + 1 ................................................ [(b^{n})^{m} = b^{nm}]

= 2^{9} / 3^{2} - 81 + 1

= 512/9 - 80

= 512/9 - 720/9 ................................................... (Multiplying & Dividing the second term with 9 to make the denominators equal)

= 512 - 720 / 9

= -208/9

= -23.11

Final Answer:-

∴ Value of given expression, when simplified is -208/9 or -23.11.

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