Laws of exponents

What is the negative exponent rule?

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

• A negative exponent means the base is negative.

• A negative exponent indicates that the base is zero.

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

What is @@10^0@@?

• 0

• 1

• 10

• Undefined

What is the difference of exponents rule?

• When multiplying like bases, add the exponents: @@rac{a^m}{a^n} = a^{m+n}@@.

• When dividing like bases, subtract the exponents: @@rac{a^m}{a^n} = a^{m-n}@@.

• When raising a power to a power, multiply the exponents: @@(a^m)^n = a^{m+n}@@.

• When adding exponents, the bases must be the same: @@a^m + a^n = a^{m+n}@@.

What is the power of a quotient rule?

• If @@a@@ and @@b@@ are real numbers and @@n@@ is a positive integer, then @@\frac{a}{b}^n = \frac{a^n}{b^n}@@.

• If @@a@@ and @@b@@ are real numbers and @@n@@ is a positive integer, then @@\frac{a}{b}^n = \frac{b^n}{a^n}@@.

• If @@a@@ and @@b@@ are real numbers and @@n@@ is a positive integer, then @@\frac{a}{b}^n = a^n + b^n@@.

• If @@a@@ and @@b@@ are real numbers and @@n@@ is a positive integer, then @@\frac{a}{b}^n = a^n - b^n@@.

What is the value of @@2^0@@?

• 0

• 1

• 2

• -1

What is the power of a product rule?

• If @@a@@ and @@b@@ are real numbers and @@n@@ is a positive integer, then @@ (ab)^n = a^n b^n @@.

• If @@a@@ and @@b@@ are real numbers, then @@ (ab)^n = a^n + b^n @@.

• If @@a@@ and @@b@@ are real numbers, then @@ (ab)^n = a^n - b^n @@.

• If @@a@@ and @@b@@ are real numbers and @@n@@ is a positive integer, then @@ (ab)^n = a^n / b^n @@.

What is the zero exponent rule?

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

• Any number raised to the power of zero equals zero.

• Any non-zero number raised to the power of one equals zero.

• Any number raised to the power of zero equals one.

What is @@5^2@@?

• 20

• 24

• 25

• 30

Simplify @@3^2 × 3^{33}@@.

• @@3^{34}@@

• @@3^{35}@@

• @@3^{36}@@

• @@3^{32}@@

What is the product of @@(-7x^2)@@ and @@4x^4@@?

• -28x^6

• -28x^4

• 28x^6

• -11x^6