Dividing, Negative, and Zero Exponents

Front

What is the rule for dividing powers with the same base?

Back

When dividing powers with the same base, subtract the exponents: a^m / a^n = a^(m-n).

Front

What does a negative exponent represent?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^-n = 1/a^n.

Front

What is the value of any non-zero number raised to the power of zero?

Back

Any non-zero number raised to the power of zero equals 1: a^0 = 1.

Front

Simplify the expression: x^5 / x^2

Back

x^(5-2) = x^3.

Front

Rewrite using a positive exponent: 3y^-4

Back

3/y^4.

Front

What is the result of 0 raised to any positive exponent?

Back

0 raised to any positive exponent is 0: 0^n = 0 (for n > 0).

Front

What is the result of 0 raised to the power of 0?

Back

0^0 is considered indeterminate in mathematics.

Front

Simplify the expression: (a^3 * a^2) / a^4

Back

a^(3+2-4) = a^1 = a.

Front

What is the rule for multiplying powers with the same base?

Back

When multiplying powers with the same base, add the exponents: a^m * a^n = a^(m+n).

Front

Simplify: (2x^-3)(3x^2)

Back

6/x.