Question

if 2^4*4^2=16^x, then find the value of x.

Answer 1

Answer:

2 is the required value of x.

Step-by-step explanation:

Explanation:

Given that, $2^4$ × $4^2$ = $16^x$

This can be written as,

  $2^4$ × $(2^2)^2$ = $(2^4)^x$

• As we know that, $(a^m)^n = a^{mn}$ is the power rule for exponents. Multiply the exponent by the power to raise a number with an exponent to that power.

• Rule of the Negative Exponent: $x^{-n}$  = $\frac{1}{x^n}$ . To make a negative exponent positive, invert the base.

Step 1:

⇒   $2^4$ × $(2^2)^2$ = $(2^4)^x$

⇒ $2^4 . 2^4 = 2^{4x}$

Now, as we know that power is added if the base is the same.

⇒ $2^{4+4} = 2^{4x}$

⇒ $2^8 = 2^{4x}$

Now, on comparing both sides we get,

⇒ 8 = 4x

⇒ x = $\frac{8}{4}$ = 2

Final answer:

Hence, 2 is the required value of x

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Answer 2

The value of $x$ is 2.

Step-by-step explanation:

Given:

The expression $2^{4} \times 4^{2} =16^{x}$

To Find:

The value of $x$.

Formula Used:

$(b^{p} )^{q} = b^{pq}$  that  is called the power rule for exponents. Multiply the exponent by the power to raise a number with an exponent to that power.

Solution:

As given, the expression $2^{4} \times 4^{2} =16^{x}$.

$2^{4} \times 4^{2} =16^{x}$

$2^{4} \times (2^{2} )^{2} =(2^{4} )^{x}$

Applying  rule of exponents  $(b^{p} )^{q} = b^{pq}$.

$2^{4} \times 2^{4} =2^{4x}$

Applying  rule of exponents $b^{p}\times b^{q} = b^{p+q}$ .

$2^{4+4} =2^{4x}$

$2^{8} =2^{4x}$

Comparing 2 power on both sides, we get.

$4x=8$

$x=\frac{8}{4}$

$x=2$

Thus, the value of $x$ is 2.

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