Knowee
Questions
Features
Study Tools

Simplify. Express your answer as the given base raised to a single exponent.(310)10

Question

Simplify. Express your answer as the given base raised to a single exponent.

(310)10(310)_{10}

🧐 Not the exact question you are looking for?Go ask a question

Solution

1. Break Down the Problem

We need to simplify (310)10 (310)_{10} and express it as a base raised to a single exponent.

2. Relevant Concepts

To simplify a number in a given base, we typically look for the prime factorization of the number.

3. Analysis and Detail

First, we find the prime factorization of 310 310 .

  • Start by dividing 310 310 by 2 2 : 310÷2=155 310 \div 2 = 155

  • Next, divide 155 155 by 5 5 : 155÷5=31 155 \div 5 = 31

  • Finally, 31 31 is a prime number.

So, the prime factorization of 310 310 is: 310=2151311 310 = 2^1 \cdot 5^1 \cdot 31^1

4. Verify and Summarize

Since 310 310 is composed of different primes and cannot be expressed as a single base raised to a power, we cannot simplify 310 310 to a single exponent term.

Final Answer

The expression (310)10 (310)_{10} cannot be simplified to a single base raised to an exponent; it remains 310=2151311 310 = 2^1 \cdot 5^1 \cdot 31^1 .

This problem has been solved

Similar Questions

orWatch a videoSimplify. Express your answer as the given base raised to a single exponent.(94)8

Simplify. Express your answer as the given base raised to a single exponent.(26)4

What is the simplified value of the exponential expression 27^(1/3)?

For the quotient of numbers: if the bases are the same, the exponents are ....multiplieddividedsubtractedadded

The of an exponential expression tells how many times the base is multiplied by itself.

1/2

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.