Q:
# What Method Is Used for Dividing Negative Exponents?

**Because a negative exponent turns the base into its reciprocal, a simple method for dividing negative exponents is letting the negative cancel and multiplying by the positive exponential expression.** Regents Prep notes that when multiple exponents have the same base, the terms can be easily divided or multiplied because the exponents themselves can be added or subtracted.

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The positive exponent k states that k amount of the bases are multiplied together. For example, 2^3 = 2*2*2 = 8.

The exponent -k states that 1 is divided by the base k times. For example, 3^(-1) = 1/3 and 3^(-4) = 1/(3*3*3*33) = 1/81. A base to a negative exponent is equal to one divided by that base to the absolute value of the exponent, such that 3^(-4) = 1/(3^4).

Math Is Fun explains that to multiply by negative exponent, one can divide by the positive exponent. For example, (4^3) * (4^(-2)) = (4^3) * 1/(4^2) = (4^3)/(4^2).

To divide by a negative exponent, one treats it like a positive exponent being multiplied. For example (4^3)/(4^(-2)) = (4^3) * 1/(4^(-2)) = (4^3) * 1/(1/(4^2)) because a negative exponent is the reciprocal of the positive, it equals (4^3) * (4^2).

If the exponential expressions have the same base, the exponents can be added when the bases are multiplied and subtracted when the bases are divided. When dividing a negative exponent, one is subtracting a negative number, which behaves like an added positive number.

For example, (4^3) * (4^2) = 4^5. Similarly, (4^3) / (4^(-2)) = 4^5.

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