Laws of Exponents Quiz

Exponents

• Exponents are also known as indices or powers.

Exponent Notation

• The notation 82 means 8 raised to the power of 2, or 8 squared.
• Any number raised to the power of 0 equals 1.

Negative Exponents

• When a number has a negative exponent, it becomes a reciprocal (i.e., 1 divided by the number).

Laws of Exponents

• The key to understanding the Laws of Exponents is to recognize that exponents are a shorthand for repeated multiplication.
• One of the Laws of Exponents is not "x^m × x^n = x^(m+n+c)", where c is a constant.

Power of a Power

• When applying the law (xm)n = xmn, we end up multiplying 'x' mn times.

Product of Powers

• According to the law (xy)n = xnyn, (xy)3 equals to x3y3.

Quotient of Powers

• The result of x2/x2 according to the law xm/xn = xm-n is 1 (since 2-2 = 0).

Power of a Product

• In the law xm/n = n√xm = (n√x)m, x(mn) equals to (n√x)m.
• According to the law (x/y)n = xn/yn, the result of (x/y)3 is x3/y3.

Fractional Exponents

• The value of x1/n, where n is a positive integer, is the nth root of x.

Simplifying Exponents

• When simplifying x(mn) using the law x(mn) = x(m × 1/n), the result is x(m/n).