Front

What is exponential notation?

Back

Exponential notation is a way to express repeated multiplication of the same number. It is written in the form a^n, where 'a' is the base and 'n' is the exponent.

Front

How do you simplify an expression with exponents, such as (a^m)(a^n)?

Back

To simplify (a^m)(a^n), you add the exponents: a^(m+n).

Front

What is the result of (7^2m^9n^3)^7?

Back

The result is 7^{14}m^{63}n^{21}, obtained by multiplying the exponents.

Front

Which expression is NOT equal to 1?

Back

(-1)^-3 is NOT equal to 1; it equals -1.

Front

How do you simplify the expression 7x - 14 - 2(4x + 8)?

Back

First, distribute the -2: 7x - 14 - 8x - 16. Then combine like terms to get -x - 30.

Front

What is the result of adding the polynomials (-3x + 4) and (8x - 5)?

Back

The result is 5x - 1, obtained by combining like terms.

Front

How do you multiply two expressions with the same base, such as a^m * a^n?

Back

To multiply two expressions with the same base, you add the exponents: a^(m+n).

Front

What is the product of a^6b^7 and a^4b^6?

Back

The product is a^{10}b^{13}, obtained by adding the exponents of like bases.

Front

What is the rule for simplifying negative exponents?

Back

The rule for negative exponents states that a^-n = 1/(a^n), where 'a' is not zero.

Front

What does it mean to simplify an expression?

Back

To simplify an expression means to reduce it to its simplest form, combining like terms and applying mathematical rules.