Lesson 5 Homework Practice Negative Exponents Answer Key (2024)

FAQs

How to solve for negative exponents? ›

The negative sign on an exponent means the reciprocal. Think of it this way: just as a positive exponent means repeated multiplication by the base, a negative exponent means repeated division by the base. So 2^(-4) = 1/(2^4) = 1/(2*2*2*2) = 1/16. The answer is 1/16.

A negative exponent is defined as the multiplicative inverse of the base, raised to the power which is of the opposite sign of the given power. In simple words, we write the reciprocal of the number and then solve it like positive exponents. For example, (2/3)^-2 can be written as (3/2)².

The negative exponent means take the reciprocal, or flip the fraction, so, ( (-27)^-1/3) / 1 = 1 / ( (-27)^1/3), and the negative exponent is now a positive exponent.

Negative exponents denote a reciprocal value. A number raised to a negative power is equal to one over the number raised to the positive opposite power. Example: x^-2 = 1/x^2.

To remove the negative exponent in an expression, the base is inverted by taking its reciprocal, and the exponent then becomes positive.

Negative exponent rule: To change a negative exponent to a positive one, flip it into a reciprocal.

For example: (-2)^3 = -2 * -2 * -2 = -8. The answer is negative because our exponent is odd. -(3)^4 = -3 * -3 * -3 * -3 = 81.

Answer and Explanation:

2 to the negative 3rd power is 1/8, or . 125 in decimal form. This can easily be calculated if one remembers that 2 to the 3rd power is 8. Since the exponent is negative, one takes the reciprocal of 8.

While positive exponents indicate repeated multiplication, negative exponents represent repeated division. That's why 2^-3 is greater than 2^-6. Flip the base and exponent into the reciprocal, then solve the denominator. Divide the numerator by the denominator to find the final decimal.

What is the negative exponent rule? ›

The negative exponent rule states that the base must be written as its reciprocal, and then the exponent will become positive. 10 to the negative power of 2 is rewritten as 1/10 to the power of 2. 10 to the power of 2 is 100, so 10 to the negative power of 2 is 1/100.

A negative exponent is defined as the multiplicative inverse of the base raised to the positive opposite of the power: x−n=1xn. Here, x is the base and −n is the negative exponent.

Answer and Explanation:

2 to the negative 3rd power is 1/8, or . 125 in decimal form.

Explanation: The negative sign in the -2 exponent implies that the number changes sides in a fraction. In other words, the 4−2 would move to the denominator. It would simplify to 142 , or 116 .

Expressions with fractional or negative exponents can be factored by pulling out a GCF. Look for the variable or exponent that is common to each term of the expression and pull out that variable or exponent raised to the lowest power. These expressions follow the same factoring rules as those with integer exponents.