Pre-Algebra Examples

${(d^{5})}^{2} = d^{10}$

Step 1

Multiply the exponents in ${(d^{5})}^{2}$ .

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Step 1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$d^{5 \cdot 2} = d^{10}$

Step 1.2

Multiply $5$ by $2$ .

$d^{10} = d^{10}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$d \approx - 50, - 49.9, - 49.65, - 49.55, - 49.475, - 49.05, - 48.925, - 48.85, - 48.7, - 48.4, - 48.2, - 48.05, - 47.7, - 47.1, - 47, - 46.9, - 46.5, - 46.1\overline{9}, - 46.0\overline{9}, - 46, - 45.8\overline{9}, - 45.6\overline{9}, - 45.4\overline{9}, - 45, - 44.5\overline{9}, - 44.0\overline{9}, - 43.6\overline{9}, - 43.44\overline{9}, - 43.2765625, - 43.174\overline{9}, - 43, - 42.8\overline{9}, - 42.7\overline{9}, - 42.5\overline{9}, - 42.0\overline{9}, - 41.8\overline{9}, - 41.5\overline{9}, - 41.3\overline{9}, - 41.2\overline{9}, - 40.724\overline{9}, - 40.4\overline{9}, - 40.2\overline{9}, - 40, - 39.8\overline{9}, - 39.5\overline{9}, - 39.3\overline{9}, - 39.17734375, - 39, - 38.6\overline{9}, - 38.5\overline{9}, - 38.3\overline{9}, - 38.1\overline{9}, - 37.5\overline{9}, - 37.4124\overline{9}, - 37.34\overline{9}, - 37.274\overline{9}, - 36.5\overline{9}, - 36.474\overline{9}, - 36, - 35.874\overline{9}, - 35.5\overline{9}, - 35.4\overline{9}, - 35.2\overline{9}, - 35.0\overline{9}, - 34.84\overline{9}, - 34.6\overline{9}, - 34.4\overline{9}, - 34.2\overline{9}, - 34.1874\overline{9}, - 34, - 33.4\overline{9}, - 33.1\overline{9}, - 32.7\overline{9}, - 32.5\overline{9}, - 32.3\overline{9}, - 32.2\overline{9}, - 32, - 31.64\overline{9}, - 31.54\overline{9}, - 31.474\overline{9}, - 31.374\overline{9}, - 31.1\overline{9}, - 30.924\overline{9}, - 30.84\overline{9}, - 30.6\overline{9}, - 30.3\overline{9}, - 30.2874\overline{9}, - 30.0\overline{9}, - 30, - 29.8\overline{9}, - 29.7\overline{9}, - 29.3\overline{9}, - 29.1\overline{9}, - 28.96874\overline{9}, - 28.7\overline{9}, - 28.6\overline{9}, - 28.3\overline{9}, - 28.2\overline{9}, - 28, - 27.8\overline{9}, - 27.5\overline{9}, - 27.4\overline{9}, - 27.2\overline{9}, - 27.0\overline{9}, - 27, - 26.94\overline{9}, - 26.774\overline{9}, - 26.54\overline{9}, - 26.3\overline{9}, - 26, - 25.774\overline{9}, - 25.5\overline{9}, - 25.3\overline{9}, - 25.0\overline{9}, - 24.9359375, - 24.84\overline{9}, - 24.774\overline{9}, - 24.6124\overline{9}, - 24.4\overline{9}, - 24.3\overline{9}, - 24.1\overline{9}, - 24, - 23.6\overline{9}, - 23.3\overline{9}, - 23.34\overline{9}, - 23.2874\overline{9}, - 22.7\overline{9}, - 22.6\overline{9}, - 22.54\overline{9}, - 22.3\overline{9}, - 22.0\overline{9}, - 22, - 21.890624\overline{9}, - 21.7874\overline{9}, - 21.674\overline{9}, - 21.4\overline{9}, - 21.3\overline{9}, - 21.2\overline{9}, - 21.2203125, - 21.14\overline{9}, - 21.04\overline{9}, - 20.8\overline{9}, - 20.6\overline{9}, - 20.4\overline{9}, - 20.2\overline{9}, - 20.11015625, - 20, - 19.74\overline{9}, - 19.64\overline{9}, - 19.578124\overline{9}, - 19.34\overline{9}, - 19.224\overline{9}, - 19.0874\overline{9}, - 18.7\overline{9}, - 18.64\overline{9}, - 18.4\overline{9}, - 18.374\overline{9}, - 18.0\overline{9}, - 18, - 17.7\overline{9}, - 17.5\overline{9}, - 17.2\overline{9}, - 17, - 16.890624\overline{9}, - 16.7124\overline{9}, - 16.5\overline{9}, - \frac{33}{2}, - 16.3\overline{9}, - 16.0\overline{9}, - 16, - 15.7\overline{9}, - 15.6\overline{9}, - \frac{31}{2}, - 15.1\overline{9}, - 14.8\overline{9}, - 14.6624\overline{9}, - \frac{29}{2}, - 14.3\overline{9}, - 14.1\overline{9}, - 13.8\overline{9}, - 13.7\overline{9}, - \frac{55}{4}, - 13.64\overline{9}, - \frac{27}{2}, - 13.3\overline{9}, - 12.8\overline{9}, - 12.7\overline{9}, - 12.6\overline{9}, - 12.5\overline{9}, - \frac{62}{5}, - 12, - 11.6\overline{9}, - \frac{58}{5}, - \frac{23}{2}, - \frac{57}{5}, - \frac{45}{4}, - 11.14\overline{9}, - 11.074\overline{9}, - 10.8\overline{9}, - 10.6\overline{9}, - 10.590624\overline{9}, - 10.44\overline{9}, - 10.34\overline{9}, - \frac{41}{4}, - \frac{81}{8}, - 10, - 9.8625, - 9.7, - \frac{48}{5}, - 9.55, - 9.421875, - 9.275, - 9, - 8.9, - 8.85, - 8.7, - \frac{17}{2}, - \frac{41}{5}, - 8, - 7.76875, - 7.165625, - 7, - 6.9, - \frac{34}{5}, - 6.65, - 6, - 5.9, - \frac{11}{2}, - 5.1, - 5.05, - 4.9, - \frac{24}{5}, - \frac{23}{5}, - \frac{9}{2}, - \frac{22}{5}, - 4.3, - 4.1, - 3.9, - \frac{19}{5}, - 3.7, - \frac{17}{5}, - 3.3, - \frac{16}{5}, - 3.1, - 3, - 2.9, - \frac{14}{5}, - \frac{13}{5}, - \frac{12}{5}, - 2.3, - \frac{11}{5}, - 2, - 1.9, - \frac{9}{5}, - \frac{8}{5}, - \frac{3}{2}, - \frac{7}{5}, - 1.3, - \frac{6}{5}, - 1.1, - 1, - 0.9, - \frac{4}{5}, - 0.7, - \frac{2}{5}, - 0.3, - 0.1, 0, 0.1, 0.3, \frac{1}{2}, \frac{3}{5}, 0.7, \frac{4}{5}, 0.9, 1.1, \frac{6}{5}, 1.3, \frac{3}{2}, \frac{9}{5}, \frac{11}{5}, 2.3, \frac{13}{5}, 2.7, 3, 3.1, \frac{16}{5}, \frac{7}{2}, 3.7, \frac{19}{5}, 3.9, 4, \frac{21}{5}, 4.3, \frac{22}{5}, \frac{9}{2}, \frac{23}{5}, 4.7, \frac{24}{5}, 4.9, 5.1, 5.225, 5.3375, \frac{11}{2}, 5.7, 5.9, 5.9375, 6.1, \frac{32}{5}, \frac{13}{2}, 6.7, 6.9, 7, 7.1, 7.3, \frac{15}{2}, 7.7, 7.85, 8, \frac{41}{5}, 8.3, 8.496875, \frac{43}{5}, 8.7, 8.9, 9, 9.1, 9.3, \frac{48}{5}, 9.7, 9.9, 10.1, \frac{21}{2}, 10.7, 10.9, 11.059375, \frac{89}{8}, \frac{57}{5}, \frac{58}{5}, 11.7, \frac{95}{8}, 12.05, 12.2, \frac{25}{2}, 12.7, 12.8, 12.9, 13, 13.1, 13.3, \frac{27}{2}, 13.8, 14, 14.1, 14.1421875, 14.4, 14.6, 14.8, 15, 15.2, 15.4, \frac{31}{2}, 15.7, 16.3, 16.6, 16.7125, 16.85, 16.9625, 17.4, 17.8, 18.3, 18.45, 18.8, 19.075, 19.125, 19.25, 19.4, 19.55, 20, 20.35, 20.45, 20.55625, 20.7625, 21.1, 21.3, 21.4, 21.6, 21.7375, 22.3, 22.475, 22.525, 22.7, 23.1, 23.3, 23.7, 24.1, 24.4, 24.5, 24.8, 25, 25.175, 25.26503906, 25.33125, 25.5, 25.6, 25.7, 25.8, 25.9125, 26.5, 27.5, 27.75, 27.9, 28, 28.1, 28.5, 28.6, 28.7, 28.859375, 29, 29.1, 29.3, 29.4, 29.65625, 29.9, 30.2, 30.4, 30.7, 30.8, 30.9, 31.1, 31.3, 31.7, 32, 32.15, 32.3, 32.4375, 32.6, 33, 33.3, 33.475, 33.55, 33.9, 34.1, 34.4, 34.575, 34.7, 35, 35.2, 35.4, 35.6, 35.8, 36, 36.1, 36.5, 36.8, 37, 37.2, 37.4, 37.5, 38, 38.5, 38.7, 39.025, 39.2, 39.3, 39.5, 39.8, 40, 40.5, 40.7, 40.9, 41.3, 41.425, 41.525, 41.7, 41.8, 42, 42.5, 43, 43.1, 43.3, 43.7, 44, 44.2, 44.4, 44.6, 44.9375, 45.3, 45.4, 45.5, 45.6, 45.85, 46, 46.2, 46.3, 46.5, 46.65, 46.8, 46.9, 47.1, 47.2, 47.4, 47.6, 47.8, 47.9, 48.1, 48.5, 48.65, 48.7625, 49, 49.2, 49.4, 49.65, 49.9$

Step 3