What is the value of n in this equation? 7^6⋅7^3=7^n Enter your answer in the box. n =
2 answers:
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The value remains under the radical is 8 ⇒ last answer
Step-by-step explanation:
Let us revise how to write the exponent as a radical
can be written as
- To simplify the radical factorize the base "a" to its prime factors
Example:
,
- Factorize 54 into prime factors ⇒ 54 = 2 × 3 × 3 × 3 =
- 2² can not go out the radical because 2 is less than 3 not divisible by 3
can go out the radical because 6 is divisible by 3, then divide 6 by 3, so it will be 3² out the radical
Now let us solve your problem
∵
- Factorize 1250 to its prime factors
∵ 1250 = 2 × 5 × 5 × 5 × 5
∴
∴
∵ 2³ can not go out the radical because 3 < 4 and not divisible by it
- can go out the radical because 12 can divided by 4
∵ 12 ÷ 4 = 3
∴ can go out the radical as 5³
∴
∴
∴ The value remains under the radical = 8
The value remains under the radical is 8
Learn more:
You can learn more about the radicals in brainly.com/question/7153188
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