Exponent Rules (Simple Laws of Exponents)

What is the product rule for exponents?

• When multiplying like bases, subtract the exponents: a^m × a^n = a^(m-n).

• When multiplying like bases, add the exponents: a^m × a^n = a^(m+n).

• When multiplying like bases, multiply the exponents: a^m × a^n = a^(m*n).

• When multiplying like bases, divide the exponents: a^m × a^n = a^(m/n).

What is the power of a power rule?

• When raising a power to another power, add the exponents: (a^m)^(n) = a^(m+n).

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

• When raising a power to another power, subtract the exponents: (a^m)^(n) = a^(m-n).

• When raising a power to another power, divide the exponents: (a^m)^(n) = a^(m/n).

What is the result of @@\frac{x^5}{x^2}@@?

• @@x^2@@

• @@x^3@@

• @@x^4@@

• @@x^5@@

What does x^5 mean?

• x⋅x⋅x⋅x⋅x

• x^2

• 5x

• x+x+x+x+x

What is the result of @@x^5 \times x^{-2}@@?

• @@x^2@@

• @@x^3@@

• @@x^4@@

• @@x^1@@

Simplify (-8r^5)(r^8).

• -8r^{12}

• -8r^{13}

• -8r^{14}

• -8r^{15}

What is the result of @@ (4a^2)(2a^3) @@?

• 6a^5

• 8a^5

• 10a^5

• 12a^5

What is the zero exponent rule?

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

• Any number raised to the power of zero equals zero: a^0 = 0.

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

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

What is the negative exponent rule?

• A negative exponent indicates the reciprocal: a^{-n} = 1/a^n.

• A negative exponent means the base is negative.

• A negative exponent indicates that the number is less than one.

• A negative exponent means to multiply the base by itself.

What is the result of @@x^3 \times x^4@@?

• @@x^6@@

• @@x^5@@

• @@x^7@@

• @@x^8@@