Select ALL the statements about the number 2^−3
that are true.
2−3
is equal to −8
.
2 to the negative 3 power is equal to negative 8 .
2−3
is less than 1.
2 to the negative 3 power is less than 1.
2−3
raised to the third power equals 1.
2 to the negative 3 power raised to the third power equals 1.
2−3
multiplied by −1
equals 23
.
2 to the negative 3 power multiplied by negative 1 equals 2 cubed.
2−3
is greater than 3−2
.
2 to the negative 3 power is greater than 3 to the negative 2 power.
To determine which statements about 2^(-3) are true, let's break down each statement and evaluate them:
Statement 1: "2^(-3) is equal to -8."
To evaluate this statement, we need to calculate 2^(-3). Remember that a negative exponent indicates taking the reciprocal of the base raised to the positive exponent. So, 2^(-3) is equal to 1 / 2^3, which simplifies to 1 / 8. Therefore, this statement is false. 2^(-3) is not equal to -8.
Statement 2: "2 to the negative 3 power is equal to negative 8."
This statement is a rephrasing of the previous statement and is also false. 2^(-3) is not equal to -8.
Statement 3: "2^(-3) is less than 1."
To evaluate this statement, we compare 2^(-3) to 1. Since 2^(-3) is equal to 1/8, it is indeed less than 1. Therefore, this statement is true.
Statement 4: "2 to the negative 3 power is less than 1."
This statement is equivalent to the previous statement and is also true. 2^(-3) is indeed less than 1.
Statement 5: "2^(-3) raised to the third power equals 1."
To evaluate this statement, we need to simplify (2^(-3))^3. Using the exponentiation rule, this simplifies to 2^(-3*3) or 2^(-9). Since 2^(-9) is not equal to 1, this statement is false. (2^(-3))^3 is not equal to 1.
Statement 6: "2 to the negative 3 power multiplied by -1 equals 2^3."
To evaluate this statement, we calculate -1 * 2^(-3), which simplifies to -1/8. This is not equal to 2^3, which is 8. Therefore, this statement is false. -1 * 2^(-3) is not equal to 2^3.
Statement 7: "2^(-3) is greater than 3^(-2)."
To evaluate this statement, we compare 2^(-3) to 3^(-2). 3^(-2) is equal to 1 / 3^2, which is 1 / 9. 2^(-3), on the other hand, is 1 / 8. Since 1/8 is greater than 1/9, this statement is true. 2^(-3) is indeed greater than 3^(-2).
Therefore, the true statements about 2^(-3) are:
- "2^(-3) is less than 1."
- "2 to the negative 3 power is less than 1."
- "2^(-3) is greater than 3^(-2)."