MCQ
Which power of $8$ is equal to $2^6?$
- A$3$
- ✓$2$
- C$1$
- D$4$
✓
Answer
Correct option: B.
$2$
Let power of $8$ be $x$.
According to the question,
$8^{\text{x}=2^{6}}$
$\Rightarrow(2)^{3\text{x}}=2^{6}$ $\big[\because8=2\times2\times2=2^{3}\big]$
$\Rightarrow2^{3\text{x}}=2^{6}$ $\big[\because(\text{a}^{\text{m}})^{\text{n}}=\text{a}^{\text{m}\times\text{n}}\big]$
Since, base equal, then by eqyating their exponents, we get
$3\text{x}=6$
$\Rightarrow\frac{3\text{x}}{3}=\frac{6}{3}$ [dividing both sides by $3$]
$\Rightarrow \text{x}=2$
Hence, the power of $8$ is $2,$ which is equal to $2^6$
According to the question,
$8^{\text{x}=2^{6}}$
$\Rightarrow(2)^{3\text{x}}=2^{6}$ $\big[\because8=2\times2\times2=2^{3}\big]$
$\Rightarrow2^{3\text{x}}=2^{6}$ $\big[\because(\text{a}^{\text{m}})^{\text{n}}=\text{a}^{\text{m}\times\text{n}}\big]$
Since, base equal, then by eqyating their exponents, we get
$3\text{x}=6$
$\Rightarrow\frac{3\text{x}}{3}=\frac{6}{3}$ [dividing both sides by $3$]
$\Rightarrow \text{x}=2$
Hence, the power of $8$ is $2,$ which is equal to $2^6$
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