Exponent Rules

Front

What is the quotient rule for exponents?

Back

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

Front

How do you simplify the expression -14x^7 / 7x?

Back

-2x^6, by applying the quotient rule and simplifying the coefficients.

Front

What happens to a base raised to the power of zero?

Back

Any non-zero base raised to the power of zero equals 1.

Front

Can a negative exponent be left in the final answer?

Back

No, negative exponents should be converted to positive by taking the reciprocal.

Front

What is the product rule for exponents?

Back

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

Front

What is the value of 5^0?

Back

1, because any non-zero number raised to the power of zero is 1.

Front

How do you simplify x^5 / x^3?

Back

x^2, by applying the quotient rule (5-3=2).

Front

What is the power of a power rule for exponents?

Back

When raising a power to another power, multiply the exponents: (a^m)^n = a^(m*n).

Front

What is the value of a^0 if a = 0?

Back

Undefined, because 0 raised to the power of zero is indeterminate.

Front

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

Back

When multiplying powers with the same exponent, multiply the bases: a^m * b^m = (a*b)^m.