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What is a rational exponent?

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A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root. For example, x^(1/2) is the square root of x.

Tags

CCSS.HSN.RN.A.2

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How do you simplify expressions with rational exponents?

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To simplify expressions with rational exponents, convert the rational exponent to a radical form and simplify the radical if possible. For example, x^(3/2) can be written as √(x^3).

Tags

CCSS.HSN.RN.A.2

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What is the relationship between rational exponents and roots?

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Rational exponents represent roots. For example, x^(1/n) represents the n-th root of x.

Tags

CCSS.HSN.RN.A.2

Front

How do you solve equations involving rational exponents?

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To solve equations with rational exponents, isolate the variable and raise both sides of the equation to the reciprocal of the rational exponent.

Front

What is the product rule for exponents?

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

Tags

CCSS.8.EE.A.1

Front

What is the power rule for exponents?

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

Tags

CCSS.8.EE.A.1

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What is the quotient rule for exponents?

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

Tags

CCSS.8.EE.A.1

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How do you evaluate expressions with rational exponents?

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To evaluate expressions with rational exponents, convert the exponent to radical form and compute the value. For example, to evaluate 8^(2/3), find the cube root of 8 and then square the result.

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What is the significance of the base in exponential expressions?

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The base in exponential expressions determines the value being raised to a power, and it affects the growth rate of the function.

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How do you find the roots of a polynomial function?

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To find the roots of a polynomial function, set the function equal to zero and solve for the variable using factoring, the quadratic formula, or numerical methods.