Question

3 power 5×10 power 5 × 25/5 power 7×6 power 5


answer quick ​

Answer 1

Answer: it’s a pleasure to help you friend.

Step-by-step explanation:

$3^{5}$ × $10^{5}$ × $(( \frac{25}{5} )^{7 * 6} )^{5}$

⇒ $a^{m}$ × $b^{m}$ = $ab^{m}$

Step 1 : As $\frac{25}{5}$ is in fraction we have to convert them into a whole number.

⇒ $\frac{25}{5}$ = 5

So, $((\frac{25}{5})^{7 * 6 } )^{5} = ((5)^{7 * 6} )^{5})$

As, 7 × 6 = 42.

⇒ $((5)^{7 * 6} )^{5} = ((5)^{42} )^{5}$

So, = $3^{5}$ × $10^{5}$ × $(((5)^{42} )^{5})$

Step 2 : according to laws of exponents , $a^{m} * b^{m} = ab^{m}$.

So, $3^{5} * 10 ^{5} * (((5^{42})^ 5$ = (3 × 10 × $5^{42}$)$)^{5}$

= (3 × 10 × 5 power 42)^ 5 = (30 × 5 power 42 ) ^ 5

= (15 × 5 ^ 21 ) ^ 5 ( we cancelled 30 and 42 by 2 ).

= (75 ^ 21 )^ 5 ( we can cancel 75 by 5 )

= 15 ^ 21

∴ The answer is $(15) ^{21}$.

Hope it’s useful friend…

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