MCQ
Write the correct answer in the following: Value of $(256)^{0.16} \times(256)^{0.09}$ is.
- ✓$4$
- B$16$
- C$64$
- D$256.25$
✓
Answer
Correct option: A.
$4$
$(256)^{0.16}\times(256)^{0.09}=(256)^{\frac{16}{100}}\times(256)^{\frac{9}{100}}$
$=(256)^{\frac{16}{100}+\frac{9}{100}}\ [\because\text{x}^\text{a}\cdot\text{x}^{\text{b}}=\text{x}^{\text{a+b}}]$
$(256)^{\frac{25}{100}}=(256)^{\frac{1}{4}}$
$=(4^4)^{\frac{1}{4}}=4\ [\because(\text{a}^\text{m})^\text{n}=\text{a}^\text{mn}]$
$=(256)^{\frac{16}{100}+\frac{9}{100}}\ [\because\text{x}^\text{a}\cdot\text{x}^{\text{b}}=\text{x}^{\text{a+b}}]$
$(256)^{\frac{25}{100}}=(256)^{\frac{1}{4}}$
$=(4^4)^{\frac{1}{4}}=4\ [\because(\text{a}^\text{m})^\text{n}=\text{a}^\text{mn}]$
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