MCQ
$(256)^{0.16} \times(256)^{0.09}$
- ✓$4$
- B$16$
- C$64$
- D$256.25$
✓
Answer
Correct option: A.
$4$
We have to find the value of $(256)^{0.16} \times(256)^{0.09}$. So,
By using law of rational exponents
$ a^m \times a^n=a^{m+n} \text { we get } $
$ (265)^{0.16} \times(256)^{0.09}=(256)^{0.16} \times(256)^{0.09} $
$ =(256)^{0.16+0.09} $
$ =256^{0.25} $
$=256^{\frac{25}{100}}$
$(256)^{0.16}\times(256)^{0.09 }=2^{8\times\frac{25}{100}}$
$=2^{8\times\frac{25}{100}}$
$=2^{8\times\frac{1}{4}}$
$=2^{8\times\frac{1}{4}}=4$
The value of $(256)^{0.16} \times(256)^{0.09}$ is $4$
Hence the correct choice is a.
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