[tex]\sf 2^{-6}[/tex]
these two options apply
[tex]\rightarrow \sf \dfrac{1}{2^6}[/tex]
[tex]\rightarrow \sf 2^{-2} \ * \ 2^4 \ * \ 2^{-8}[/tex]
in decimals : 0.015625
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.
⇒ [tex]2^{-6}[/tex]
⇒ [tex]\frac{1}{2^{-6} }[/tex]
Now, change the exponent's sign.
⇒ [tex]\frac{1}{2^{-6} }[/tex]
⇒ [tex]\frac{1}{2^{6} }[/tex]
Now, simplify the term.
⇒ [tex]\frac{1}{2^{6} }[/tex]
⇒ [tex]\frac{1}{2 \times 2 \times 2 \times 2 \times 2 \times 2} }[/tex]
⇒ [tex]\frac{1}{8 \times 8}[/tex]
⇒ [tex]\frac{1}{64}[/tex]
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.
[tex]-2^{6} \rightarrow -2 \times -2 \times -2 \times -2 \times -2 \times -2[/tex]
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.
[tex]-2 \times -2 \times -2 \times -2 \times -2 \times -2[/tex]
⇒ [tex]2 \times 2 \times 2 \times 2 \times 2 \times 2[/tex]
⇒ [tex]64[/tex]
[tex]-2^{6} = 64 \neq \frac{1}{64}[/tex]
B)------------------------------------------------------------------------------------------------------
Since -64 is already a simplified term, we can compare this with the simplified result.
[tex]-64 \neq \frac{1}{64}[/tex]
C)------------------------------------------------------------------------------------------------------
[tex]\frac{1}{2^{6}}[/tex]
⇒ [tex]\frac{1}{2 \times 2 \times 2 \times 2 \times 2 \times 2 }[/tex]
⇒ [tex]\frac{1}{8 \times 8 }[/tex]
⇒ [tex]\frac{1}{64}[/tex]
[tex]\frac{1}{2^{6} } = \frac{1}{64} = \frac{1}{64}[/tex]
D)------------------------------------------------------------------------------------------------------
[tex]2^{-2} \times 2^{4} \times 2^{-8}[/tex]
⇒ [tex]\frac{1}{2^{2}} } \times 16 \times \frac{1}{2^{8} }[/tex]
⇒ [tex]\frac{1}{4} \times 16 \times \frac{1}{256}[/tex]
⇒ [tex]\frac{1}{4} \times 1 \times \frac{1}{16}[/tex] [16² = 256]
⇒ [tex]\frac{1}{4} \times \frac{1}{16}[/tex]
⇒ [tex]\frac{1}{64}[/tex]
[tex]2^{-2} \times 2^{4} \times 2^{-8} = \frac{1}{64} = \frac{1}{64}[/tex]
E)------------------------------------------------------------------------------------------------------
[tex]2^{3} \times 2^{-2}[/tex]
⇒ [tex]2^{3 - 2}[/tex]
⇒ [tex]2^{1} = 2[/tex]
[tex]2^{3} \times 2^{-2} = 2 \neq \frac{1}{64}[/tex]
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