Simplifying Exponents

Front

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

Back

To multiply two exponential expressions with the same base, add their exponents. For example, a^m * a^n = a^(m+n).

Front

How do you simplify the expression (-4r^5)(2r^8)?

Back

Multiply the coefficients (-4 * 2 = -8) and add the exponents of r (5 + 8 = 13), resulting in -8r^13.

Front

What is the quotient rule for exponents?

Back

The quotient rule states that when dividing two exponential expressions with the same base, subtract the exponent of the denominator from the exponent of the numerator. For example, a^m / a^n = a^(m-n).

Front

How do you evaluate the expression x^5 / x^2 using the quotient rule?

Back

Using the quotient rule, subtract the exponents: x^5 / x^2 = x^(5-2) = x^3.

Front

What is the power of a power rule in exponents?

Back

The power of a power rule states that when raising an exponential expression to another exponent, multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

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

Back

Apply the power of a power rule: (2^2)^5 = 2^(2*5) = 2^10 and (y^3)^5 = y^(3*5) = y^15. Thus, (2^2y^3)^5 = 1024y^15.

Front

What is the result of simplifying x^5 * x^7?

Back

Add the exponents since the bases are the same: x^5 * x^7 = x^(5+7) = x^12.

Front

How do you simplify the expression 9^5 / 9^2 using the quotient rule?

Back

Using the quotient rule, subtract the exponents: 9^5 / 9^2 = 9^(5-2) = 9^3.

Front

What is the value of 2^10?

Back

2^10 = 1024.

Front

What does it mean to simplify an expression with exponents?

Back

Simplifying an expression with exponents means to rewrite it in a more compact or manageable form, often by applying exponent rules.