Exponents

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 expressions 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 quotient of powers property?

Back

The quotient of powers property states that when dividing two expressions with the same base, you subtract the exponents. For example, a^m / a^n = a^(m-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

Calculate: (3^2)^4

Back

(3^2)^4 = 3^(2*4) = 3^8 = 6561.

Front

Calculate: 5^3 × 5^2

Back

5^3 × 5^2 = 5^(3+2) = 5^5 = 3125.

Front

Calculate: 7^5 / 7^2

Back

7^5 / 7^2 = 7^(5-2) = 7^3 = 343.

Front

Calculate: (x^4)^3

Back

(x^4)^3 = x^(4*3) = x^12.