To simplify a fractional power like $a^{\\frac{m}{n}}$, you take the [ ] and the $m$th power.","back":"To simplify a fractional power like $a^{\\frac{m}{n}}$, you take the $n$th root and the $m$th power.","points":null},{"id":"5d031d17-8086-4fa0-934d-6a165b2e40dd","cardType":"cloze","front":"To simplify a fractional power like $a^{\\frac{m}{n}}$, you take the $n$th root and the [ ].","back":"To simplify a fractional power like $a^{\\frac{m}{n}}$, you take the $n$th root and the $m$th power.","points":null},{"id":"18052ef9-c9c5-4cf0-a764-ce1569a4e7a0","cardType":"basic","front":"How do you rewrite $27^{2x-1}$ as a power of 3?","back":"$$(3^3)^{2x-1} = 3^{3(2x-1)}$","points":1},{"id":"4c0c1cb3-46d3-44df-9b42-c991eb10fc04","cardType":"cloze","front":"When simplifying $(a^m)^n$, you must [ ] the indices together.","back":"When simplifying $(a^m)^n$, you must multiply the indices together.","points":null},{"id":"b9426767-c3c9-4f0c-af0d-3cdcefff5699","cardType":"basic","front":"What is the common base for an equation containing $8^x$ and $4^x$?","back":"Base 2 ($2^3$ and $2^2$)","points":1},{"id":"0572816f-8da2-4de5-a6ce-56f6e12293e5","cardType":"basic","front":"What substitution converts $4^x - 10(2^x) + 16 = 0$ into a quadratic equation?","back":"Let $y = 2^x$ (giving $y^2 - 10y + 16 = 0$)","points":2},{"id":"b049afc5-ae7e-48ae-8732-e0ab2e8815ee","cardType":"basic","front":"If solving an exponential equation via substitution $y = a^x$, why must a result of $y = -2$ be rejected?","back":"An exponential term $a^x$ (where $a > 0$) is always positive.","points":2},{"id":"66b1590c-c01d-468d-a046-1121fbd01b9b","cardType":"cloze","front":"The expression $2^{2x}$ is equivalent to the square of $\\text{[...]}$.","back":"The expression $2^{2x}$ is equivalent to the square of $\\boxed{2^x}$.","points":null},{"id":"474b205e-e333-44f8-9c13-3d3fc88bb1d1","cardType":"basic","front":"What are the two main steps to factorise $6x - 24x^3$ completely?","back":"

Factorise out the highest common factor ($6x$)
Apply difference of two squares to $(1 - 4x^2)$

","points":2},{"id":"873ffc67-9c21-41cc-9837-65174bb91e8e","cardType":"cloze","front":"A negative fractional index like $\\left(\\frac{a}{b}\\right)^{-\\frac{1}{2}}$ indicates you should first take the [ ] of the fraction.","back":"A negative fractional index like $\\left(\\frac{a}{b}\\right)^{-\\frac{1}{2}}$ indicates you should first take the reciprocal of the fraction.","points":null},{"id":"0ff5e075-1af0-44e5-8715-d3e6b2d7917b","cardType":"basic","front":"Expand and simplify $(x + 1)^2$.","back":"$$x^2 + 2x + 1$","points":1},{"id":"16b0ee32-8fa4-4ddb-8683-c49f71bd4127","cardType":"basic","front":"What is the conjugate of $a + \\sqrt{b}$ used in rationalising denominators?","back":"$$a - \\sqrt{b}$","points":1},{"id":"a7b32917-b555-462a-94ec-7b1ff5db18d4","cardType":"cloze","front":"Multiplying a denominator by its conjugate rationalises it by creating a [ ].","back":"Multiplying a denominator by its conjugate rationalises it by creating a difference of two squares.","points":null},{"id":"5bc0cba0-ddef-4581-a5d0-682bbac17998","cardType":"basic","front":"How do you solve for $x$ in an equation like $\\frac{2 + x}{x} = \\sqrt{5}$?","back":"

Multiply by $x$ to clear the fraction
Collect $x$ terms on one side and factorise out $x$
Divide by the coefficient bracket

","points":2},{"id":"c9a4da40-7bb2-42d2-9546-a552d168

Algebraic Expressions Flashcards

Algebraic Expressions Flashcards

Algebraic Expressions Flashcards

Algebraic Expressions Flashcards