Question

Write 7 3 × √ 7 as a single power of 7.

Answer 1

Answer:

7^3.5

Step-by-step explanation:

so √7 can also be written as 7^1/2 and so u can add the powers so 7^3 + 7^1/2 is 7^3.5

Answer 2

$\displaystyle \sf{ {7}^{3} \times \sqrt{7} = \bf {7}^{ \frac{7}{2} } }$

Correct question : Write 7³ × √7 as a single power of 7.

Given :

The expression 7³ × √7

To find :

Write 7³ × √7 as a single power of 7.

Formula :

We are aware of the formula on indices that :

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

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is 7³ × √7

Step 2 of 2 :

Express as a single power of 7

$\displaystyle \sf{ {7}^{3} \times \sqrt{7} }$

$\displaystyle \sf{ = {7}^{3} \times {7}^{ \frac{1}{2} } }$

$\displaystyle \sf{ = {7}^{(3 + \frac{1}{2}) } }\: \: \: \bigg[ \: \because \:{a}^{m} \times {a}^{n} = {a}^{m + n} \bigg]$

$\displaystyle \sf{ = {7}^{ \frac{(6+1)}{2}} }$

$\displaystyle \sf{ = {7}^{ \frac{7}{2}} }$

$\boxed{ \: \: \displaystyle \sf{ {7}^{3} \times \sqrt{7} = {7}^{ \frac{7}{2} } } \: \: }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ Using law of exponents, simplify (5²)³÷5³

https://brainly.in/question/36250730

2. If 2x× 4x=(8)1/3 × (32)1/5 ,then find the value of x

https://brainly.in/question/14155738

#SPJ3