Laws of Exponents Review

What is the negative exponent rule?

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

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

• A negative exponent indicates that the base is negative.

• A negative exponent means to add the exponent to the base.

What is the definition of an exponent?

• An exponent indicates how many times to multiply the base by itself.

• An exponent is a number that represents the square root of a base.

• An exponent is a symbol used to denote a fraction of a base.

• An exponent is a term used to describe the logarithm of a base.

Simplify: @@ (x^2y)^5 @@

• @@ x^{10}y^{5} @@

• @@ x^{10}y^{6} @@

• @@ x^{5}y^{10} @@

• @@ x^{2}y^{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 power of a quotient rule in exponents?

• When raising a quotient to a power, apply the exponent to both the numerator and denominator: (a/b)^n = a^n / b^n.

• The exponent applies only to the numerator: (a/b)^n = a^n / b.

• The exponent applies only to the denominator: (a/b)^n = b^n / a.

• The exponent is ignored when dealing with quotients: (a/b)^n = a/b.

What is the power of a power rule in exponents?

• 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).

Simplify: @@ (2x^3)^4 @@

• @@ 8x^{9} @@

• @@ 16x^{12} @@

• @@ 4x^{10} @@

• @@ 32x^{15} @@

What is the definition of a coefficient in an expression?

• A coefficient is a numerical factor in a term of an expression.

• A coefficient is a variable that represents a constant value.

• A coefficient is an operation performed on two numbers.

• A coefficient is a type of polynomial expression.

What is the power of a product rule in exponents?

• When raising a product to a power, apply the exponent to each factor: (ab)^n = a^n * b^n.

• The exponent applies only to the first factor in the product: (ab)^n = a^n * b.

• The product of the exponents is equal to the exponent of the product: (ab)^n = a * b^n.

• The exponent is distributed equally among the factors: (ab)^n = (a^n)(b^n).