Laws of Exponents

Click on the flashcard to see the answer



What is the product rule in exponents?

The product rule states that when multiplying two exponents with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

How do you apply the power rule to exponents?

The power rule states that when you raise a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

What is the quotient rule in exponents?

The quotient rule states that when dividing exponents with the same base, you subtract the exponents. For example, a^m / a^n = a^(m-n).

Explain a zero exponent.

Any number raised to the zero power is equal to 1, except for zero itself. For example, a^0 = 1.

What happens when you have a negative exponent?

A negative exponent represents a reciprocal. For example, a^(-n) = 1/a^n.

How do you simplify (a^m)^0?

Any nonzero base to the zero power is 1, so (a^m)^0 = 1.

What is the rule for multiplying two equal bases but with negative exponents?

Add the exponents, including their negative signs. For example, a^(-m) * a^(-n) = a^(-m-n).

What does (x^m * y^m) equal?

(x^m * y^m) is equal to (xy)^m.

How do you express b^(-n) as a fraction?

b^(-n) is expressed as 1/b^n.

What does it mean for exponents to be distributive over multiplication?

It means that (xy)^n = x^n * y^n.

If a^5 = 1, what can you say about a?

a must be equal to 1 if a^5 = 1, assuming a is a positive real number.

Can you simplify (x^3 / x^3)?

Yes, (x^3 / x^3) equals x^(3-3) = x^0 = 1.

What is (k^4)^-1 in simplest form?

(k^4)^-1 is equal to 1/(k^4).

How would you simplify ((a^2)^3)^4?

You multiply the exponents: 2 * 3 * 4 = 24, so ((a^2)^3)^4 = a^24.

If b^(m/n) = x, how can this be rewritten using roots?

b^(m/n) can be rewritten as the n-th root of b^m, or (root(n)(b))^m.