Exponent Rules

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, 3 is the exponent.

Front

In the expression 3^16 = (3^8)(3^?) what is the missing exponent?

Back

The missing exponent is 8, because 3^16 = 3^8 * 3^8.

Front

What is the product of 5^3 and 5^4?

Back

The product is 5^7, because when multiplying like bases, you add the exponents: 3 + 4 = 7.

Front

How do you simplify the expression \frac{10x^{15}}{2x^3}?

Back

You simplify it to 5x^{12} by dividing the coefficients (10/2) and subtracting the exponents (15-3).

Front

What is the result of x^2 \cdot x^4?

Back

The result is x^6, because when multiplying like bases, you add the exponents: 2 + 4 = 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}. For example, (x^2)^3 = x^{2*3} = x^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 (where a ≠ 0).

Front

What is the product of powers rule?

Back

The product of powers rule states that a^m * a^n = a^{m+n}. For example, 2^3 * 2^2 = 2^{3+2} = 2^5.

Front

What is the quotient of powers rule?

Back

The quotient of powers rule states that a^m / a^n = a^{m-n}. For example, 5^7 / 5^3 = 5^{7-3} = 5^4.

Front

What is the definition of a base in exponents?

Back

The base is the number that is being multiplied by itself in an exponential expression. In 4^2, 4 is the base.