Input in the form: xab Show
Enter the value of “x” : Answer Rational Exponents Calculator is a free online tool that displays the value for the given rational exponent expression. BYJU’S online rational exponents calculator tool makes the calculation faster, and it displays the value in a fraction of seconds. How to Use the Rational Exponents Calculator?The procedure to use the rational exponents calculator is as follows: Step 1: Enter the base and rational exponent in the respective input field Step 2: Now click the button “Solve” to get the result Step 3: Finally, the value of the rational exponents expression will be displayed in the output field What is Meant by Rational Exponents?In maths, the rational number is of the form a/b. Rational exponent means the exponent number should be in the form of a rational number. It is also known as the fractional exponents. In this case, an integer is found in the numerator and the root is found in the denominator. For example, 41/2 Where 4 is the base ½ is the rational exponent Calculator UseUse this calculator to find the fractional exponent of a number x. With fractional exponents you are solving for the dth root of the number x raised to the power n. For example, the following are the same: \( 4^{\frac{3}{2}} = \sqrt[2]{4^{3}} \) and since 4 cubed equals 64 we get \( = \sqrt[2]{64} = \pm 8 \) Notes on Fractional Exponents:This online calculator puts calculation of both exponents and radicals into exponent form.
For more detail on Exponent Theory see Mathworld Exponent Laws. Radicals (square roots, cube roots, fourth roots, and so on) can be rewritten as rational exponents (exponents which are fractions) using the relationship {eq}\sqrt[n]{x} = x^{\frac{1}{n}} {/eq}. More generally, using the power rule of exponents, {eq}\sqrt[n]{x^m} = (x^m)^{\frac{1}{n}} = x^{\frac{m}{n}} {/eq}. This means that the denominator of a rational exponent indicates the type of radical being used - a denominator of 3 indicates a cube root, a denominator of 4 indicates the fourth root, and so on. We will walk through three examples that demonstrate how to convert between radical expressions and expressions containing rational exponents. Example Problem 1: Converting Between Radicals and Rational ExponentsRewrite the following radical expressions using a rational exponent.
Since the type of radical corresponds with the denominator of a rational exponent, we know the denominator of the exponent will be 7. Therefore, {eq}\sqrt[7]{8^4} = 8^{\frac{4}{7}} {/eq}. For the second problem, since we have a ninth root, the denominator of the rational exponent will be 9. Therefore, {eq}\sqrt[9]{3^{10}} = 3^{\frac{10}{9}} {/eq}. Example Problem 2: Converting Between Radicals and Rational ExponentsRewrite the following rational exponent expressions in radical form.
Since the denominator of a rational exponent corresponds with the type of radical, we know that we have a fifth root for the radical. Therefore, {eq}3^{\frac{2}{5}} = \sqrt[5]{3^2} {/eq}. In the second problem, the denominator of the rational exponent is a 4, so we have a fourth root. Therefore, {eq}7^{\frac{9}{4}} = \sqrt[4]{7^9} {/eq}. Example Problem 3: Converting Between Radicals and Rational Exponents
{eq}\sqrt[3]{x^8} = x^{\frac{8}{3}}\\ x^{\frac{6}{7}} = \sqrt[7]{x^6} {/eq} Get access to thousands of practice questions and explanations! What is radical form to exponential form?Radicals (square roots, cube roots, fourth roots, and so on) can be rewritten as rational exponents (exponents which are fractions) using the relationship n√x=x1n x n = x 1 n . More generally, using the power rule of exponents, n√xm=(xm)1n=xmn x m n = ( x m ) 1 n = x m n .
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Converting between radical form and exponent form calculator
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