Question

Find the value of (7/2)⁸ * (7/2)⁶​

Answer 1

${ (\frac{7}{2} })^{8} \times { (\frac{7}{2} })^{6} \\ \\ \pink{ {a}^{m} \times {a}^{n} = {a}^{m + n} } \\ \\ \red{hence} \\ \\ { (\frac{7}{2} })^{8 + 6} \\ \\ { (\frac{7}{2} })^{14}$

Answer 2

Given:

$(\frac{7}{2} )^{8}$ × $(\frac{7}{2} )^{-6}$

To find :

The value of $(\frac{7}{2} )^{8}$ × $(\frac{7}{2} )^{-6}$

Formula to be used:

$a^{m}$ × $a ^{n}$ = $a^{m+n}$

Solution:

In a product of powers property, when multiplying two powers with the same base,we add the exponents.

$a^{m}$ × $a ^{n}$ = $a^{m+n}$

In this value, $(\frac{7}{2} )^{8}$ × $(\frac{7}{2} )^{-6}$

The base are same. So we can add the exponents.

$(\frac{7}{2} )^{8}$ × $(\frac{7}{2} )^{-6}$ = $(\frac{7}{2} )^{8-6}$

$(\frac{7}{2} )^{8}$ × $(\frac{7}{2} )^{-6}$ = $(\frac{7}{2} )^{2}$

$(\frac{7}{2} )^{8}$ × $(\frac{7}{2} )^{-6}$ = $\frac{49}{4}$

Final answer:

The value of $(\frac{7}{2} )^{8}$ × $(\frac{7}{2} )^{-6}$ is $\frac{49}{4}$