# MAT - Paper 2018 - Q1G

> Source: https://ollybritton.com/notes/maths/problems/mat/2018/q1g/ · Updated: 2025-01-17 · Tags: mat, notes, maths

## Flashcards
### 2021-10-27
##### If you're worried about how a $\pm$ has cropped up, how can you sometimes safely only consider it as negative or as positive??
By looking about what is true in a sketch.

$$x^5 = 2$$
What is $x$ using fractional exponents??::
$$
x = 2^{\frac{1}{5}}
$$

$$x^{-4} = 6$$ What is $x$ using fractional exponents??::
$$
x = 6^{-\frac{1}{4}}
$$

$$x^{\frac{3}{2}} = 4$$ What is $x$ using fractional exponents??::
$$
x = 4^{\frac{2}{3}}
$$

$$x^{\frac{a}{b}} = 7$$ What is $x$ using fractional exponents??::
$$
x = 7^{\frac{b}{a}}
$$

$$x^{\frac{3}{2}} = \frac{1}{4}$$ Solve for $x$??::
$$
x = \frac{1}{4^{\frac{2}{3}}}
$$

For $f(x)$ and $g(x)$ to touch, what two things must be true??::
$$
f'(x) = g'(x)
$$

$$
f(x) = g(x)
$$

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