What is 9 to the -3 power in standard form?
The Correct Answer and Explanation is :
To find (9) raised to the power of (-3), we start with the expression:
[
9^{-3}
]
The negative exponent indicates that we take the reciprocal of the base raised to the absolute value of the exponent. Therefore, we can rewrite the expression as:
[
9^{-3} = \frac{1}{9^3}
]
Next, we need to calculate (9^3). This means multiplying (9) by itself three times:
[
9^3 = 9 \times 9 \times 9
]
Calculating (9 \times 9) first gives us (81). Now, we multiply (81) by (9):
[
81 \times 9 = 729
]
Thus, we have:
[
9^3 = 729
]
Now we can substitute this back into our expression for (9^{-3}):
[
9^{-3} = \frac{1}{729}
]
The standard form of a number typically refers to expressing it in a straightforward manner, and since (\frac{1}{729}) is already in a clear, concise format, we can present it as:
[
9^{-3} = \frac{1}{729}
]
Summary
In summary, (9^{-3}) simplifies to (\frac{1}{9^3}). Calculating (9^3) yields (729), leading us to the final answer of:
[
9^{-3} = \frac{1}{729}
]
This process illustrates the importance of understanding negative exponents, which are commonly used in various mathematical and scientific contexts. Negative exponents help express very small numbers or fractions concisely, making them particularly useful in fields such as physics, engineering, and finance.