Simplifying Exponential Expressions

Front

What is the product of two exponential expressions with the same base?

Back

When multiplying two exponential expressions with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

How do you simplify an expression with a negative exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, a^{-n} = 1/(a^n).

Front

What is the quotient rule for exponents?

Back

When dividing two exponential expressions with the same base, you subtract the exponents. For example, a^m / a^n = a^(m-n).

Front

How do you simplify the expression a^m * a^n?

Back

You add the exponents: a^m * a^n = a^(m+n).

Front

What is the value of x in the equation 3^{16}=(3^8)(3^x)?

Back

x = 8, because you can set the exponents equal: 16 = 8 + x.

Front

What does it mean to raise a power to another power?

Back

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

Front

How do you simplify the expression (-3y^{-5})^{-2}?

Back

You take the reciprocal of the base and square it, resulting in y^{10}/9.

Front

What is the simplified form of 1/a^n?

Back

The simplified form is a^{-n}, which indicates the reciprocal of a raised to the power n.

Front

What is the value of 5 in the context of exponential expressions?

Back

In exponential expressions, 5 can represent a base or an exponent, depending on the context.

Front

What is the zero exponent rule?

Back

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