Question

Solve for n.
B. (15^n)7 ×15^n =15^16

Answer 1

Answer:

n=2

Step-by-step explanation:

(15^n)7 ×15^n =15^16

=15^ 7n x 15^n =15^16

15^(7n+n)=15^16

15^8n=15^16

so 8n=16

n=2

Answer 2

SOLUTION

TO DETERMINE

The value of n when

$\sf{{( {15}^{n} )}^{7} \times {15}^{n} = {15}^{16} }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

$\sf{1. \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

$\sf{2. \: \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

EVALUATION

Here the given equality is

$\sf{{( {15}^{n} )}^{7} \times {15}^{n} = {15}^{16} }$

We now solve for n

$\sf{{( {15}^{n} )}^{7} \times {15}^{n} = {15}^{16} }$

$\sf{ \implies \: {(15)}^{7n} \times {15}^{n} = {15}^{16} } \: \: \: \: \: (by \: formula \: 1)$

$\sf{ \implies \: {(15)}^{7n + n} = {15}^{16} } \: \: \: \: \: (by \: formula \: 2)$

$\sf{ \implies \: {(15)}^{8n} = {15}^{16} } \: \: \: \:$

$\sf{ \implies \: 8n = 16}$

$\sf{ \implies \: n = 2}$

FINAL ANSWER

The required value of n is 2

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If 2x× 4x=(8)1/3 × (32)1/5 ,

then find the value of x

https://brainly.in/question/14155738

2. Evaluate:

7 x 7^1/2 x 7^1/4 x 7^1/8 ..to infinity

https://brainly.in/question/20308189