Question

What is the value of 12 power 6 times the reciprocal of 6 power 7?

Answer 1

Hope this helps you

Answer 2

Answer:

Value of $12^{6}\: times \:the \:reciprocal\:of\:6^{7}$

=$\frac{32}{3}$

Explanation:

Value of $12^{6}\: times \:the \:reciprocal\:of\:6^{7}$

= $12^{6}\times \frac{1}{6^{7}}$

= $(2\times6)^{6}\times \frac{1}{6^{6}}$

=$2^{6}\times6^{6}\times \frac{1}{6^{7}}$

/* By Exponential Law :

$\boxed {(ab)^{m} = a^{m}\times b^{m}}$ */

= $\frac{2^{6}}{6^{7-6}}$

/* By Exponential Law :

$\boxed {\frac{a^{m}}{a^{n}}=\frac{1}{a^{m-n}}}$ */

= $\frac{2^{6}}{6}$

= $\frac{2\times 2^{5}}{2\times3}$

=$\frac{32}{3}$

Therefore,

Value of $12^{6}\: times \:the \:reciprocal\:of\:6^{7}$

=$\frac{32}{3}$

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