1 trillion raised to the tenth power
The Correct Answer and Explanation is:
When raising 1 trillion to the 10th power, the number you get is:(1 trillion)10=(1×1012)10=10120(1 \, \text{trillion})^{10} = (1 \times 10^{12})^{10} = 10^{120}(1trillion)10=(1×1012)10=10120
This means the result is 1012010^{120}10120, which is a 1 followed by 120 zeros.
Explanation:
To understand how we get to this result, let’s break it down step by step:
- What is 1 trillion?
In scientific notation, 1 trillion is written as 1×10121 \times 10^{12}1×1012. A trillion is a 1 followed by 12 zeros, or 1,000,000,000,000. - Raising a number to an exponent:
When you raise a number to a power, you’re multiplying that number by itself the number of times indicated by the exponent. For example, 23=2×2×2=82^3 = 2 \times 2 \times 2 = 823=2×2×2=8. - Raising 1 trillion to the 10th power:
Now, if you take 1×10121 \times 10^{12}1×1012 and raise it to the 10th power, you are multiplying the number 1×10121 \times 10^{12}1×1012 by itself 10 times. This can be rewritten as: (1×1012)10=110×(1012)10(1 \times 10^{12})^{10} = 1^{10} \times (10^{12})^{10}(1×1012)10=110×(1012)10 - Simplifying the powers:
Since 110=11^{10} = 1110=1, you only need to focus on the second part, which is (1012)10(10^{12})^{10}(1012)10. According to the power of a power rule in exponents, (am)n=am×n(a^m)^n = a^{m \times n}(am)n=am×n, so: (1012)10=1012×10=10120(10^{12})^{10} = 10^{12 \times 10} = 10^{120}(1012)10=1012×10=10120
Therefore, 1 trillion10=101201 \, \text{trillion}^{10} = 10^{120}1trillion10=10120, which is the final result. This is an extremely large number, and it’s written as a 1 followed by 120 zeros. This is far beyond the scope of everyday numbers, and it illustrates how quickly numbers grow when raised to large powers.
