Laws of Exponents Review

Front

What are the 9 Laws of Exponents?

Back

1. Product of Powers: a^m * a^n = a^(m+n) 2. Quotient of Powers: a^m / a^n = a^(m-n) 3. Power of a Power: (a^m)^n = a^(m*n) 4. Power of a Product: (ab)^n = a^n * b^n 5. Power of a Quotient: (a/b)^n = a^n / b^n 6. Zero Exponent: a^0 = 1 (a ≠ 0) 7. Negative Exponent: a^(-n) = 1/a^n 8. Fractional Exponent: a^(m/n) = n√(a^m) 9. Exponent of One: a^1 = a.

Front

How do you simplify (a^4)^3 using the laws of exponents?

Back

Using the Power of a Power law: (a^m)^n = a^(m*n), we have (a^4)^3 = a^(4*3) = a^12.

Front

What is the result of simplifying (y^8)^5?

Back

Using the Power of a Power law: (y^m)^n = y^(m*n), we have (y^8)^5 = y^(8*5) = y^40.

Front

What is the value of 5^17?

Back

5^17 is a large number, specifically 5^17 = 762939453125.

Front

How do you apply the quotient rule to simplify 9^5?

Back

The quotient rule states that a^m / a^n = a^(m-n). If you have an expression like 9^m / 9^(m-5), you can simplify it to 9^(m - (m-5)) = 9^5.

Front

What does a zero exponent mean in the context of exponents?

Back

Any non-zero number raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Front

What is the significance of a negative exponent?

Back

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

Front

How do you simplify the expression (ab)^n?

Back

Using the Power of a Product law: (ab)^n = a^n * b^n.

Front

What is the result of simplifying (x^3y^2)^4?

Back

Using the Power of a Product law: (x^3y^2)^4 = x^(3*4) * y^(2*4) = x^12 * y^8.

Front

How do you simplify the expression (x/y)^3?

Back

Using the Power of a Quotient law: (x/y)^3 = x^3 / y^3.