Difficulty
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Interactive test · 25 simplifying problems, easy → medium → hard. Product, quotient, power, power-of-a-product, and zero/negative exponent rules.
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Easy Simplify: \(x^3 \cdot x^4\).
Answer: C — \(x^{7}\)
Easy Simplify and evaluate: \(2^2 \cdot 2^3\).
Answer: C — \(32\)
Easy Simplify: \(\dfrac{x^8}{x^3}\).
Answer: D — \(x^{5}\)
Easy Simplify: \((x^3)^2\).
Answer: D — \(x^{6}\)
Easy Simplify: \((2x)^3\).
Answer: A — \(8x^{3}\)
Easy Simplify: \(5x^{0}\) (assume \(x\neq 0\)).
Answer: A — \(5\)
Easy Write with a positive exponent: \(x^{-2}\).
Answer: B — \(\dfrac{1}{x^{2}}\)
Medium Simplify: \(3x^2 \cdot 4x^5\).
Answer: B — \(12x^{7}\)
Medium Simplify: \((2x^4)^3\).
Answer: B — \(8x^{12}\)
Medium Simplify: \(\dfrac{15x^6}{3x^2}\).
Answer: A — \(5x^{4}\)
Medium Simplify: \((x^2 y^3)^4\).
Answer: D — \(x^{8} y^{12}\)
Medium Simplify: \((a^3)^2 \cdot a\).
Answer: D — \(a^{7}\)
Medium Simplify: \((3x^2)^2\).
Answer: C — \(9x^{4}\)
Medium Evaluate \(2^{-3}\). (Enter a fraction or decimal.)
\(=\)Answer: \(\dfrac{1}{8}\)
Medium Simplify: \(\left(\dfrac{x^5}{x^2}\right)^{3}\).
Answer: B — \(x^{9}\)
Medium Write with a positive exponent: \(4x^{-3}\).
Answer: D — \(\dfrac{4}{x^{3}}\)
Hard Simplify with positive exponents: \((2x^3 y^{-2})^{3}\).
Answer: B — \(\dfrac{8x^{9}}{y^{6}}\)
Hard Simplify with positive exponents: \(\dfrac{12x^5 y^2}{4x^2 y^5}\).
Answer: D — \(\dfrac{3x^{3}}{y^{3}}\)
Hard Simplify: \(\dfrac{(3x^2)^3}{9x^4}\).
Answer: A — \(3x^{2}\)
Hard Simplify: \(\dfrac{(2x^2)^3 \cdot x}{4x^4}\).
Answer: D — \(2x^{3}\)
Hard Simplify with positive exponents: \((x^{-2} y^{3})^{-2}\).
Answer: D — \(\dfrac{x^{4}}{y^{6}}\)
Hard Evaluate \(5x^{0} + 3\) for any \(x\neq 0\).
\(=\)Answer: \(8\)
Hard Simplify: \((a^2 b)^3 (a b^2)^2\).
Answer: D — \(a^{8} b^{7}\)
Hard Evaluate \(\dfrac{2^{-2}}{2^{-4}}\).
\(=\)Answer: \(4\)
Hard Simplify with positive exponents: \(\dfrac{x^{7} y^{-3}}{x^{2} y^{-5}}\).
Answer: C — \(x^{5} y^{2}\)