Question
Find the value of $(1296)^{0.17}\times(1296)^{0.08}.$
✓
Answer
$(1296)^{0.17}\times(1296)^{0.08}$
$=(6^4)^{\frac{17}{100}}\times(6^4)^{\frac{8}{100}}$
$=6^{4\times\frac{17}{100}}\times6^{4\times\frac{8}{100}}$
$=6^{\frac{17}{25}}\times6^{\frac{8}{25}}$
$=6^{\frac{17}{25}+\frac{8}{25}}$
$=6^{\frac{25}{25}}$
$=6$
$=(6^4)^{\frac{17}{100}}\times(6^4)^{\frac{8}{100}}$
$=6^{4\times\frac{17}{100}}\times6^{4\times\frac{8}{100}}$
$=6^{\frac{17}{25}}\times6^{\frac{8}{25}}$
$=6^{\frac{17}{25}+\frac{8}{25}}$
$=6^{\frac{25}{25}}$
$=6$
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