CIA 2 Review

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, x^a * x^b = x^(a+b).

Front

How do you simplify an expression with a negative exponent?

Back

To simplify an expression with a negative exponent, you take the reciprocal of the base raised to the positive exponent. For example, x^{-n} = 1/x^n.

Front

What is scientific notation and why is it used?

Back

Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10. It is used to simplify the representation of very large or very small numbers.

Front

How do you divide exponential expressions with the same base?

Back

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

Front

What is the power of a power property in exponents?

Back

The power of a power property states that when raising an exponent to another exponent, you multiply the exponents. For example, (x^a)^b = x^(a*b).

Front

How do you simplify a fraction with exponents?

Back

To simplify a fraction with exponents, subtract the exponent in the denominator from the exponent in the numerator if the bases are the same. For example, (x^a)/(x^b) = x^(a-b).

Front

What is the square root of a fraction?

Back

The square root of a fraction is the square root of the numerator divided by the square root of the denominator. For example, √(a/b) = √a / √b.

Front

How do you evaluate a square root of a fraction?

Back

To evaluate a square root of a fraction, simplify the fraction first if possible, then take the square root of the numerator and the denominator separately.

Front

What is the relationship between exponents and roots?

Back

Exponents and roots are inversely related; for example, raising a number to a fractional exponent corresponds to taking a root. For example, x^(1/n) = √[n]{x}.

Front

What does it mean to express an answer in scientific notation?

Back

Expressing an answer in scientific notation means writing it in the form a × 10^n, where 1 ≤ a < 10 and n is an integer.