Question

The simplified form of an expression is StartFraction 1 Over 256 EndFraction t Superscript 28. Which expression was simplified?


A.(256 t Superscript negative 7 Baseline) Superscript 4

B.(4 t Superscript 28 Baseline) Superscript negative 4

C.(256 t Superscript negative 7 Baseline) Superscript negative 4

D.(4 t Superscript negative 7 Baseline) Superscript negative 4

Answer 1

Answer:

1/258 *(t^28)

= t^28 / 4^4

= t^28 4^-4

= (t^-7 * 4)^-4

= (4t^-7)^-4

Answer 2

The simplified form of an expression   $\frac{1}{256} * t^{28}$ will be $(4 t^{-7})^{-4}$ which is given in option number $(D)$ i.e. ($4\ t$ Superscript negative $7$ Baseline) Superscript negative $4$ .

What is  simplified form ?

Simplified form a rational expression is considered simplified if the numerator and denominator have no factors in common.

We have,

 $\frac{1}{256} * t^{28}$

Now to simplify it,

Convert $256$ into a exponent form with a base.

i.e.

$\frac{1}{4^4} * t^{28}$

Now,

Using the exponent rule;

$\frac{1}{a^n}= a^{(-n)}$

So,

$4^{-4}\ *\ t^{28}$

Now, simplify it more by taking common power of $4$ and $t$ ,

$(4\ *\ t^{-7})^{-4}$

⇒ $(4 t^{-7})^{-4}$

So, this is the simplified form of given expression which is given in option number $(D).$

Hence, we can say that the simplified form of an expression   $\frac{1}{256} * t^{28}$ will be $(4 t^{-7})^{-4}$ which is given in option number $(D)$ i.e. ($4\ t$ Superscript negative $7$ Baseline) Superscript negative $4$ .

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