Question
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Simplify the expression. Write your answer as a power. \( \begin{array}{ll}\text { A. } 4 \cdot 4^{5}=4^{6} & \text { B. } 6^{3} \cdot 6^{7} \\ \text { C. }(-3)^{8} \cdot(-3)^{3} & \text { D. }\left(\frac{4}{5}\right)^{2} \cdot\left(\frac{4}{5}\right)^{6} \\ \text { E. }\left(7^{3}\right)^{5} & \text { F. }\left((-8)^{10}\right)^{3} \\ \text { Simplify the expression. } \\ \text { G. }(8 a)^{3} & \text { H. }(-4 c)^{5} \\ \text { I. }(1.5 r)^{2} & \text { J. }\left(\frac{2}{3} m\right)^{4} \\ \text { K. } 3^{2} \cdot 3^{4}-4^{4} & \text { L. } 7 \cdot\left(7^{3}-7^{2}\right) \\ \text { M. }\left(\frac{1}{3}\right)^{4} \cdot\left(9^{3}\right)^{2} & \begin{array}{l}\text { N. The budget for a remake of a movie is } 100 \text { times the } \\ \text { budget of the original movie. The original movie's } \\ \text { budget was } 10^{5} \text { dollars. What is the budget of the } \\ \text { remake? Express your answer as a power. }\end{array}\end{array}{ }_{l} \)

Ask by Bob Griffin. in the United States
Mar 18,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

A: \(4^{6}\), B: \(6^{10}\), C: \((-3)^{11}\), D: \(\left(\frac{4}{5}\right)^{8}\), E: \(7^{15}\), F: \((-8)^{30}\), G: \(512a^{3}\), H: \(-1024c^{5}\), I: \(\frac{9}{4}r^{2}\), J: \(\frac{16}{81}m^{4}\), K: \(473\), L: \(2058\), M: \(3^{8}\), N: \(10^{7}\).

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The Deep Dive

For option A, \(4 \cdot 4^{5} = 4^1 \cdot 4^5 = 4^{1+5} = 4^{6}\). Keep those bases the same and just add the exponents! Now, let’s tackle option D: \(\left(\frac{4}{5}\right)^{2} \cdot \left(\frac{4}{5}\right)^{6} = \left(\frac{4}{5}\right)^{2 + 6} = \left(\frac{4}{5}\right)^{8}\). It’s all about combining those like bases! Stay on your toes for those exponent rules; they’re your best friends in simplification land!

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