Properties of Exponents

Front

What is the value of any non-zero number raised to the power of 0?

Back

1

Front

Simplify: (8^5)^3

Back

8^{15} (Use the power of a power property: a^{m*n} = a^{mn})

Front

What is the product of two powers with the same base?

Back

Add the exponents: a^m * a^n = a^{m+n}.

Front

Simplify: 3^4 ⋅ 3^7

Back

3^{11} (Add the exponents: 4 + 7 = 11)

Front

What happens to a variable raised to the power of 0?

Back

It equals 1, e.g., x^0 = 1.

Front

Simplify: 2x^0y^3

Back

2y^3 (x^0 = 1, so it simplifies to 2 * 1 * y^3)

Front

What is the value of a negative exponent?

Back

a^{-n} = 1/a^n (It represents the reciprocal of the base raised to the positive exponent)

Front

Simplify: 6^{-4}

Back

1/6^{4} (Use the negative exponent rule)

Front

What is the quotient of two powers with the same base?

Back

Subtract the exponents: a^m / a^n = a^{m-n}.

Front

Simplify: (3^2)^3

Back

3^{6} (Use the power of a power property: a^{m*n} = a^{mn})