What expressions are equal to 10 to the power of negative 5

What expressions are equal to 10 to the power of negative 5

The correct answer and explanation is:

Correct Answer:
Expressions equal to 10−510^{-5} include:

• 1105\frac{1}{10^5}
• 0.000010.00001
• 1×10−51 \times 10^{-5}

Explanation (Approx. 300 words)

The expression 10−510^{-5} is an example of a number written in scientific notation with a negative exponent. Understanding negative exponents is key to converting this into equivalent expressions.

Meaning of 10−510^{-5}:

The negative exponent tells us to take the reciprocal of the base raised to the positive exponent: 10−5=110510^{-5} = \frac{1}{10^5}

So instead of multiplying 10 by itself five times, you divide 1 by 10^5.

Step-by-step calculation:

105=10×10×10×10×10=100,00010^5 = 10 \times 10 \times 10 \times 10 \times 10 = 100,000 10−5=1100,000=0.0000110^{-5} = \frac{1}{100,000} = 0.00001

Alternative Expressions:

All of the following are mathematically equivalent to 10−510^{-5}:

1. Fraction form:
   1100,000\frac{1}{100,000}
2. Decimal form:
   0.000010.00001
3. Scientific notation:
   1×10−51 \times 10^{-5}

These forms are used in different contexts. Scientists often prefer scientific notation for very small or very large numbers because it’s more compact and readable.

Why it’s Important:

Understanding how to interpret and convert powers of 10, especially with negative exponents, is essential in math and science. It helps you work with measurements like micrometers (10−610^{-6} meters), nanoseconds (10−910^{-9} seconds), and very small concentrations in chemistry.

So, when you see 10−510^{-5}, you can confidently say it’s equal to:

• One hundred-thousandth
• 0.00001
• 1105\frac{1}{10^5}
• 1×10−51 \times 10^{-5}

All are correct and interchangeable depending on the context.