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# Find the value of each of the following: (i) 16^{1/4} (ii) 625^{(-3/4)}

Exponential notation helps us to represent extremely large and small numbers in a simple and readable manner. Exponents or powers signifies the number of times a base (integer, fraction, decimal) is multiplied by itself.

## Answer: The value of (i) 16^{1/4} = 2 and (ii) 625^{(-3/4)} = 1/125

Let us look into the steps below to solve them.

**Explanation:**

(i) 16^{1/4}

Let's represent 16^{1/4} as a base of 2.

We know that,

16 = 2^{4}

Substituting in the given expression we get,

16^{1/4} = (2^{4})^{ 1/4}

According to the power of exponent rules we have,

(a^{m})^{n} = a^{mn }

Thus,

(2^{4})^{ 1/4} = 2^{4 × (1/4)}

(2^{4})^{ 1/4} = 2

### (ii) 625^{(-3/4)}

Since, the base has a negative power we will use the exponent rules to change it to a positive power.

According to the negative property of exponents we have,

a^{-m} = 1/a^{m}

Thus,

625^{(-3/4)} = (1/625) ^{3/4}

= {(1/625) ^{1}^{/4}}^{3} (Since, (a^{m})^{n} = a^{mn })

= {(1/5^{4})^{ 1/4}}^{3} (Since, 625 = 5^{4})

= {(1/5)^{4 × (1/4)}}^{3} (Since, (a^{m})^{n} = a^{mn })

= (1/5)^{3}

= 1/5^{3} (Since, (a/b)^{m} = a^{m}/b^{m})

= 1/125

### Thus, the value of (i) 16^{1/4} = 2 and (ii) 625^{(-3/4)} = 1/125.

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