Exponent Rules

Front

What is the power of a product rule in exponents?

Back

The power of a product rule states that (ab)^n = a^n * b^n, meaning you can distribute the exponent to each factor in the product.

Front

How do you simplify (2x^3y)^6 using exponent rules?

Back

You apply the power of a product rule: (2^6)(x^(3*6))(y^6) = 64x^18y^6.

Front

What is the power of a power rule in exponents?

Back

The power of a power rule states that (a^m)^n = a^(m*n), meaning you multiply the exponents.

Front

How do you find the missing exponent in the equation 5y^2 * (2y^3)^x = 80y^14?

Back

You can set up the equation: 5 * 2^x * y^(2 + 3x) = 80y^14 and solve for x, which gives x = 4.

Front

What does it mean to rewrite an expression using positive exponents?

Back

Rewriting using positive exponents means converting any negative exponents into positive by moving them to the opposite side of the fraction.

Front

How do you simplify the expression -14x^7 / 7x?

Back

You can simplify by dividing the coefficients and subtracting the exponents: -2x^(7-1) = -2x^6.

Front

What is the zero exponent rule?

Back

The zero exponent rule states that any non-zero number raised to the power of zero equals one: a^0 = 1.

Front

What is the negative exponent rule?

Back

The negative exponent rule states that a^(-n) = 1/(a^n), meaning you can convert negative exponents to positive by taking the reciprocal.

Front

What is the product of powers rule in exponents?

Back

The product of powers rule states that a^m * a^n = a^(m+n), meaning you add the exponents when multiplying like bases.

Front

What is the quotient of powers rule in exponents?

Back

The quotient of powers rule states that a^m / a^n = a^(m-n), meaning you subtract the exponents when dividing like bases.