Question

Help for 40 points and brainliest

Answer 1

$\sf 2^{-6}$

these two options apply

$\rightarrow \sf \dfrac{1}{2^6}$

$\rightarrow \sf 2^{-2} \ * \ 2^4 \ * \ 2^{-8}$

in decimals : 0.015625

Answer 2

Answer:

Option C and D

Step-by-step explanation:

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Example:

If the given exponent is a⁻ᵇ, then the result will be 1/aᵇ.

This exponent includes a negative sign. To make the exponent positive, take the exponent's reciprocal and change the negative sign to a positive sign. The same will be done to the given expression.

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First, take the exponent's reciprocal as said above.

⇒ $2^{-6}$

⇒ $\frac{1}{2^{-6} }$

Now, change the exponent's sign.

⇒ $\frac{1}{2^{-6} }$

⇒ $\frac{1}{2^{6} }$

Now, simplify the term.

⇒ $\frac{1}{2^{6} }$

⇒ $\frac{1}{2 \times 2 \times 2 \times 2 \times 2 \times 2} }$

⇒ $\frac{1}{8 \times 8}$

⇒ $\frac{1}{64}$

Using the simplified result we obtained, let's verify all the options to see which is equivalent to the term.

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A)------------------------------------------------------------------------------------------------------

Keep in mind that the exponent is the number of times the base needs to multiply itself.

$-2^{6} \rightarrow -2 \times -2 \times -2 \times -2 \times -2 \times -2$

NOTE: If there are even number of "-", then the result should be positive. If there are odd number of "-", then the result should be negative.

$-2 \times -2 \times -2 \times -2 \times -2 \times -2$

⇒ $2 \times 2 \times 2 \times 2 \times 2 \times 2$

⇒ $64$

$-2^{6} = 64 \neq \frac{1}{64}$

B)------------------------------------------------------------------------------------------------------

Since -64 is already a simplified term, we can compare this with the simplified result.

$-64 \neq \frac{1}{64}$

C)------------------------------------------------------------------------------------------------------

$\frac{1}{2^{6}}$

⇒ $\frac{1}{2 \times 2 \times 2 \times 2 \times 2 \times 2 }$

⇒ $\frac{1}{8 \times 8 }$

⇒ $\frac{1}{64}$

$\frac{1}{2^{6} } = \frac{1}{64} = \frac{1}{64}$

D)------------------------------------------------------------------------------------------------------

$2^{-2} \times 2^{4} \times 2^{-8}$

⇒ $\frac{1}{2^{2}} } \times 16 \times \frac{1}{2^{8} }$

⇒ $\frac{1}{4} \times 16 \times \frac{1}{256}$

⇒ $\frac{1}{4} \times 1 \times \frac{1}{16}$                                                                               [16² = 256]

⇒ $\frac{1}{4} \times \frac{1}{16}$

⇒ $\frac{1}{64}$

$2^{-2} \times 2^{4} \times 2^{-8} = \frac{1}{64} = \frac{1}{64}$

E)------------------------------------------------------------------------------------------------------

$2^{3} \times 2^{-2}$

⇒ $2^{3 - 2}$

⇒ $2^{1} = 2$

$2^{3} \times 2^{-2} = 2 \neq \frac{1}{64}$

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