Exponents and Radical Roots

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, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

Front

What does a negative exponent represent?

Back

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

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What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. It is denoted as √x.

Front

How do you simplify an expression with exponents?

Back

To simplify, apply the laws of exponents, such as multiplying powers (a^m * a^n = a^(m+n)) and dividing powers (a^m / a^n = a^(m-n)).

Front

What is the product of powers rule?

Back

The product of powers rule states that when multiplying two powers with the same base, you add the exponents: a^m * a^n = a^(m+n).

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What is the quotient of powers rule?

Back

The quotient of powers rule states that when dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

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What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

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How do you convert a radical expression to an exponent?

Back

To convert a radical to an exponent, use the formula: √a = a^(1/2) and ∛a = a^(1/3).

Front

What is the power of a power rule?

Back

The power of a power rule states that when raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

What is the relationship between exponents and roots?

Back

Exponents and roots are inversely related; taking the nth root of a number is the same as raising that number to the power of 1/n.