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QLDMath MethodsQuick questions
Unit 2: Calculus
Quick questions on Indices and the laws of exponents (QCE Math Methods Unit 2)
10short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is rational exponent?Show answer
$8^{2/3} = (\sqrt[3]{8})^2 = 2^2 = 4$.
What is same base?Show answer
$2^x \cdot 2^{3x+1} = 2^{4x+1}$.
What is different bases, rewritten?Show answer
$9^{x+1} = (3^2)^{x+1} = 3^{2x+2}$, so $9^{x+1} = 3 \cdot 3^{2x+1}$.
What is adding exponents on different bases?Show answer
$2^3 \cdot 3^2$ is not $6^5$. Index laws only work when bases match.
What is misapplying the negative exponent?Show answer
$-2^4$ is $-16$, not $16$. The negative is outside the power. $(-2)^4 = 16$.
What is forgetting to align bases?Show answer
$4^x = 32$ becomes $2^{2x} = 2^5$, so $x = 5/2$.
What is treating $0^0$ as $1$?Show answer
QCAA does not test $0^0$. Avoid it; if it appears, treat it as undefined.
What is iA1?Show answer
Direct application questions: simplify a multi-term expression with mixed positive, negative and fractional exponents, or solve a same-base equation.
What is eA Paper 1?Show answer
Multiple choice on index manipulations and short solve problems.
What is eA Paper 2?Show answer
Used as the algebra step inside a larger problem (an exponential growth model, a calculus-of-exponentials computation).