Math Powers Test Practice

Simplify: \(5^{-2}\)

Write with positive exponents only: \(\dfrac{3^{-4}}{3^{2}}\)

Simplify: \((xy)^{-3}\)

Rewrite without negative exponents: \(\dfrac{8^{-1} a^{3}}{a^{-2}}\)

Simplify: \((-2)^{-3}\)

Rewrite with positive exponents only: \(\dfrac{x^{-5} y^{2}}{x^{3}}\)

Simplify: \((3a^{-2} b^{4})^{-1}\)

Write with positive exponents: \(p^{-3} q^{-2} r\)

Simplify: \(x^{7} \cdot x^{3}\)

Simplify: \(4^{5} \cdot 4^{-2}\)

Simplify: \(m^{-4} \cdot m^{10}\)

Simplify: \(2x^{3} \cdot 5x^{2}\)

Simplify: \(y^{12} \cdot y^{-15}\)

Simplify: \((3a^{2}b)(2a^{3}b^{4})\)

Simplify: \(t^{-6} \cdot t^{-4}\)

Simplify: \((-5k^{3})(-2k^{-1})\)

Simplify: \((a^{3})^{2}\)

Simplify: \((x^{-1})^{4}\)

Simplify: \(\left(\dfrac{2}{3}\right)^{3}\), then express with positive exponents only.

Simplify: \((p^{2} q^{-3})^{3}\)

Simplify: \((m^{-2} n^{4})^{2}\)

Simplify: \((4x^{3} y^{-1})^{3}\)

Simplify: \(\left(\dfrac{a^{-2}}{b^{5}}\right)^{2}\)

Simplify: \((r^{0} s^{-1})^{4}\)

Simplify: \((3xy)^{2}\)

Simplify: \(\left(\dfrac{a}{b}\right)^{-3}\)

Simplify: \((2a^{2}b^{-1})^{2}\)

Simplify: \(\left(\dfrac{5x^{-2}}{y^{3}}\right)^{2}\)

Expand and simplify: \((6m^{2}n)^{3}\)

Simplify: \(\left(\dfrac{3a^{-1}b^{2}}{2c^{-3}}\right)^{2}\)

Simplify: \((xyz^{-2})^{4}\)

Simplify: \(\left(\dfrac{4k^{-2}}{m^{3} n^{-1}}\right)^{-1}\)

Simplify completely: \(x^{-2} \cdot (x^{3})^{2}\)

Simplify completely: \(\dfrac{4^{3} \cdot 4^{-5}}{4^{-1}}\)

Simplify completely: \((a^{-1} b^{2})^{3} \cdot a^{4}\)

Simplify completely: \(\dfrac{6x^{4}y^{-2}}{3x^{-1}y^{3}}\)

Simplify completely: \((u^{-3} v^{5})^{-2} \cdot u^{4}\)

Simplify completely: \(\dfrac{(2x^{-1} y^{3})^{2}}{(4x^{2} y^{-1})}\)

Simplify completely: \((5a^{2} b^{-4})(3a^{-3}b^{2})(2a b^{-1})\)

Simplify completely: \(\left(\dfrac{p^{2}}{q^{-3}}\right)^{-2} \cdot p^{-1} q^{4}\)

Simplify: \(\left( \dfrac{x^{-2} y^{4}}{3z^{-1}} \right)^{3}\)

Simplify: \(\dfrac{(2a^{-3} b^{2})^{2}(3a b^{-4})^{-1}}{6a^{-2} b^{5}}\)

Simplify: \((x^{-1} + x^{-2})(x^{3})\) (Hint: distribute first.)

Simplify fully: \(\dfrac{4^{-2} (mn^{-3})^{-2}}{(m^{-1} n^{2})^{3}}\)

Simplify: \(\left( \dfrac{(a^{-1}b^{2})^{-2}}{(a^{3}b^{-1})} \right)^{-1}\)