(256)0.16x (256)0.09= ?a)4b)16c)64d)256.25Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Because here the basic property of exponents are used i.e. a to power multiplied by a to power n equals a to power m+n

Answer

(256)(0.16+0.09)
(256)(25/100)
(256)(1/4)
(4)4. (1/4)
=4

Answer

Given: (256)0.16x (256)0.09= ?

To solve this problem, we need to use the exponent rule that says:
a^m * a^n = a^(m+n)

Using this rule, we can simplify the expression as follows:

(256)0.16x (256)0.09 = 256(0.16x + 0.09) (applying the exponent rule)

Now, we can evaluate the expression inside the parentheses:

0.16x + 0.09 = 0.25x + 0.09 - 0.16x (combining like terms)

= 0.09 + 0.09x (simplifying)

Substituting back into the original expression, we get:

(256)0.16x (256)0.09 = 256(0.09 + 0.09x)

= 23(0.09 + 0.09x) (since 256 = 2^8 = 23)

= 2^3 * 0.09 + 2^3 * 0.09x (distributing the exponent)

= 0.72 + 2.16x

Therefore, the answer is 4 (option A) because 0.72 + 2.16x = 4 when x = 1.5.

Answer

⇒ (256)^0.16 x (256)^0.09 = (256)^{(0.16 + 0.09)}

= (256)^0.25
= (256)^{(25 / 100)}
= (256)^{(1 / 4)}
= (4⁴)^{(1 / 4)}
= 4⁴^{(1 / 4)}
= 4¹
= 4

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