Exponent Properties

Front

What is the quotient rule for exponents?

Back

When dividing two powers with the same base, subtract the exponents: a^m / a^n = a^(m-n).

Front

How do you simplify the expression x^3y / xy^5?

Back

By applying the quotient rule, you get x^(3-1) / y^(1-5) = x^2 / y^4.

Front

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

Back

It means to eliminate any negative exponents by expressing them as fractions. For example, a^-n = 1/a^n.

Front

How do you simplify the expression (2m^4)(5m^2)?

Back

Multiply the coefficients (2*5) and add the exponents of the same base: 10m^(4+2) = 10m^6.

Front

What is the value of x^-6?

Back

x^-6 = 1/x^6.

Front

What is the product rule for exponents?

Back

When multiplying two powers with the same base, add the exponents: a^m * a^n = a^(m+n).

Front

How do you simplify n⋅n^4⋅n^5?

Back

Using the product rule, you add the exponents: n^(1+4+5) = n^10.

Front

What is the power of a power rule for exponents?

Back

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

Front

How do you express 2w^-13 using positive exponents?

Back

2w^-13 = 2 / w^13.

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).