Use the Negative Exponent Rule to generate an equivalent expression to 3^(−1/2) .(1 point)
Using the negative exponent rule, we can rewrite 3^(-1/2) as 1/(3^(1/2)).
To use the Negative Exponent Rule to generate an equivalent expression to 3^(-1/2), we can rewrite it as:
1/3^(1/2)
This is because the Negative Exponent Rule states that for any nonzero number a, a^(-n) = 1/a^n. In this case, a = 3 and n = 1/2.
Therefore, the equivalent expression to 3^(-1/2) is 1/3^(1/2).
To use the Negative Exponent Rule and generate an equivalent expression, we need to remember that a negative exponent means the reciprocal of the corresponding positive exponent.
The Negative Exponent Rule states that a number raised to a negative exponent is equal to 1 divided by that number raised to the absolute value of the exponent.
In this case, we have 3 raised to the power of -1/2, so we can apply the rule as follows:
3^(-1/2) = 1 / 3^(1/2)
Now, to simplify further, we can rewrite the fraction 1/3^(1/2) so that the exponent is a positive integer.
We know that the square root of a number can be expressed as a fractional exponent. The square root of x is equivalent to x^(1/2).
Therefore, 3^(1/2) is the square root of 3, or √3.
Substituting this back into the expression:
1 / 3^(1/2) = 1 / √3
And there you have it! The equivalent expression to 3^(-1/2) is 1 / √3.