Exponents Test

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

Front

What is the product of powers property?

Back

The product of powers property states that when multiplying two powers with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

What is the power of a power property?

Back

The power of a power property states that when raising a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

What is the power of a product property?

Back

The power of a product property states that when raising a product to a power, you can distribute the exponent to each factor. For example, (ab)^n = a^n * b^n.

Front

What is the zero exponent rule?

Back

The zero exponent rule states that any non-zero base raised to the power of zero equals one. For example, a^0 = 1 (where a ≠ 0).

Front

What is the negative exponent rule?

Back

The negative exponent rule states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, a^(-n) = 1/(a^n).

Front

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

Back

x^(2+3) = x^5.

Front

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

Back

6x^(4+2) = 6x^6.

Front

Simplify: (5x^3)^2

Back

25x^(3*2) = 25x^6.

Front

Simplify: (2x^2y^3)(3xy^2)

Back

6x^(2+1)y^(3+2) = 6x^3y^5.