Question

Find the value of (256)0.16 multipied to (256)0.09

Answer 1

Given:

${(256)}^{0.16} \times {(256)}^{0.09}$

To find:

The value of multiplication of given exponents.

Solution:

To answer this question, first of all, we should know one of the properties of exponents which is- if two numbers that have the same base 'a' but different powers m and n are multiplied then in the resultant the powers are added but the base remains the same.

This means,

${a}^{m} \times {a}^{n} = {a}^{(m + n)}$

Now, we have,

${(256)}^{0.16} \times {(256)}^{0.09}$

This can be written as

${256}^{(0.16 + 0.09)}$

(from the property of exponents that has been mentioned above)

$= {256}^{(0.25)}$

$= {256}^{ (\frac{1}{4}) }$

(as 0.25 = 25/100 = 1/4)

Now,

$= {4}^{ {4}^{ (\frac{1}{4} )} }$

(as 256 = 4 × 4 × 4 × 4)

So,

$= 4$

So, the value of the given expression is 4.

Answer 2

check the answer in the above attachment

hope this helps .✓